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Let's say someone (me) is having a tough time deciding if they want to concentrate in machine learning or complexity theory. Instead of doing a masters first to explore research/coursework in both areas and then do a PhD, why not just choose one of them to do a PhD and then switch later as a Postdoc?
I'm in the USA. I have the choice of doing a masters first but i feel it might be too much time. I could save much more time by doing a phd first and then exploring later.
A professor of mine told a cautionary tale about someone he went to school with. After earning their bachelor's degree, they started working on their PhD. Around three years into the process, their project lost funding and the PhD supervisor moved to another university in a different country. The student essentially had to either start over under a new supervisor in a different subject area, or drop out and leave academia. The whole experience left such a bad taste in their mouth that they chose the latter. At that point, the student had a bachelor's degree and some graduate study but no real results to show for it.
Another student in the same research group also ended up dropping out, but they went with the masters+PhD route. They had the same coursework as the first student, comparable research work and publications, etc. but at the end of the day they also had a master's degree to show for it. The second student had a considerably easier time entering the private sector and commanded a higher salary.
The moral of the story is that if you're going to do a master's degree's worth of work, don't skip the degree. You might not need it once you get the PhD, but there are a thousand potential hurdles - many outside your control - that could trip you up before you get to the finish line. It might be different if there's not much overlap and the master's degree adds an unreasonable amount of time to the time it takes to earn the PhD, but even an extra 25-33% would (IMO) be worth the safety factor of having that additional checkpoint.
Ordinarily in the US, you apply to a post doc position as an academic-in-training under a professor's lab. This is a job: you are applying to an available position (whether it's posted ahead of time or not), and you'll do work related to the lab you join. Your qualifications are judged by the professor doing the hiring: if you've done research work as a PhD student in complexity theory, will you be able to convince a professor that you're the best applicant for a post doc in their lab doing machine learning? Maybe, especially if you can identify synergies between your expertise and what the lab is working on, but will you be a better applicant than other applicants who did their PhDs in machine learning? If you're totally green that means your potential supervisor needs to train you from the ground up. They might be willing to do that for a PhD student, but expect a post doc to come in more ready to work independently (and usually with a higher cost). Post docs are typically in a lab for much shorter time than a PhD student: a PhD student can founder for a couple years while they learn to float, but by that time a post doc's appointment has expired.
Alternatively or in concert, you can apply for some sort of post-doctoral fellowship; these fellowships primarily fund your development as a person learning to do independent research, and if you have money it's a lot easier to get a position under a mentor because they don't have to find the money to pay you. That gives you a bit of freedom, sure, but not the "freedom to work on whatever you want": you typically have to write some sort of research proposal to the granting agency. Can you convince a granting agency that your proposal to study some topic in complexity theory is among the best proposals they receive, when your past research work is all in machine learning? Will you be familiar enough with the open questions in complexity theory and be able to demonstrate your capability to address those questions with your background in machine learning? Maybe, especially if you can identify synergies between your background and the new topic, but will you be a better applicant than all the people who did their PhDs in complexity theory?
It's definitely possible to generalize and branch out in an academic career, but it is typically done incrementally, by applying your existing skills to an adjacent area, or through collaborations where each collaborator brings a different type of knowledge into a shared project. Later career academics have more flexibility in both of these areas than early career academics, because if you are aiming to build an academic career you're needing to compete first with other applicants for post docs, then with other applicants for professor positions, then put together a tenure package, etc.
In addition to the answer of Bryan Krause, note that in the US there is no need to choose between different subfields in CS in order to apply with only a bachelors. There will be plenty of time (couple of years, perhaps), early on, for coursework that lets you choose a proper research area. You also get to spend some time looking at faculty to find a dissertation advisor.
The first task in most US CS programs is to take advanced coursework that enables you to pass the qualifying exams. There are a few exceptions to that, but it is very common.
Also, as I think you understand, there is normally no need, in the US, to get a masters in order to apply for a doctorate. In fact the early coursework in a doctoral program is likely to overlap with that of a masters. If you want a PhD, then apply for that. In some other countries (Germany...) the situation is different.
So, you may have a misconception that you can "just choose one", as there is no real need to choose early, i.e. before you apply. And another misconception that you can just switch as a fresh PhD.
As to switching fields "later" I'll agree with Bryan Krause that immediately after earning a doctorate not a likely time. You need to get hired for something, maybe a postdoc, based on the skills you have demonstrated. There are probably a few postdocs that give you a lot of freedom, but that isn't the standard. Switching is easy for tenured faculty, since you have a secure base from which to explore. But that is down the road a bit.
In the US, the students who enter doctoral studies in most fields fall into a few categories. There are those who are undecided after a bachelors about their future, but want to know more. There are those who start a doctoral program in one place but leave for one of several reasons, but leave with a masters and want to continue doctoral study elsewhere (my case, actually). There are those who want to return to academia after a stint in industry for which they earned a masters. International students often come with a masters due to the system requirements in their home countries where a masters might be required for doctoral study.
But few students who actually want a doctorate in US decide to do a masters first, as it just isn't necessary. There are some, certainly, but it isn't the most common path. Partly because the goals of the two are usually different. Masters prepares practitioners. PhD prepares researchers. But, again, this is a US perspective.
See the following for more on how doctoral admissions works in the US, in case you have questions: https://academia.stackexchange.com/a/176909/75368
I don't know your age, but if you're a traditional student then you'll finish your PhD in your mid-late twenties. By then, dicking around with Postdocs and making 40k isn't going to feel like "exploring", it's going to feel like you're getting ripped off. In my opinion, postdocs are not for "exploring". They are for people who are sure they want an academic job.
If you can't decide whether you want a PhD in machine learning or complexity theory, just pick the one with a better funding situation and an advisor you get along better with. Before you start your PhD you don't really know anything about either field anyway. The student-advisor relationship is what will determine if you enjoy your PhD or not. The subject matter is secondary.
If you have strong interest in two complementary areas, some graduate institutions offer interdisciplinary Ph.D. programs.
Or select one primary degree field, but be strategic about also pursuing more than one formal course and/or research experience in the second area. Seek a degree program where this will be encouraged (or at least permitted) based on information from faculty advisors and current students.
Then you might legitimately market yourself as having expertise in both areas (reporting honestly the amount of training in each) after finishing the Ph.D. degree.
It may not save you much time so check first
In my case the school I was working on my PhD at (I didn’t finish) didn’t accept my courses from my masters at my previous school and made me retake them all (it didn’t make any sense)—so I effectively did the coursework for a masters plus the coursework for a Ph.D while still having the same expectations time wise for a PhD. It wasn’t fun and I think contributed to my burning out and leaving. So if you want to go this route make sure you understand the expectations in terms of course load. Of course by skipping a Masters you’d skip having to do a thesis, but you could still be on the hook for all the coursework, and you’d miss out on the research experience that a Masters brings.
A Masters is a good way to test the waters
Also a Masters is a much lighter lift than a PhD. There’s no guarantee that you’ll want to go for the latter and starting toward a Masters is a good way to test the waters with much less commitment.
A Masters is an asset in industry; a PhD can be a liability
If you wind up going to industry, a Masters will almost always help you by making you more marketable and raising your income. While a PhD can raise your income further (sometimes by a lot), it can close the door to many jobs in industry and pigeonhole you quite a bit. That’s not a bad thing as long as you’re sure what you want to do, but if you’re not sure yet a Masters is a safer starting point.
Switching topics isn’t going to be easy
My experience from this comes from getting into machine learning research as a switch mid-career from software development (I work in industry). I can definitively say that learning enough about a totally new domain to find a worthwhile open problem and begin to do research in it is really hard. Until you develop this expertise the Dunning-Kruger effect is in play and it seems like the problems in other fields are a piece of cake, but they’re not. I’m not writing this to discourage you from switching from time to time, just to share that doing so requires a lot of hard work to learn the new subject very very deeply, so don’t expect it to be easy.
