I understand your concern, but you have a couple of things backwards.
While, in theory, when it comes to papers, you could write these yourself and you don't need your supervisor*, when it comes to grants, however, it's a completely different story. I'm speaking from a UK perspective and terminology here, but I assume similar practices apply elsewhere.
Unfortunately, in practical terms, there is absolutely no way for you to apply for a traditional grant as a PI at your stage, and are unlikely to for a long time. This is because funding bodies tend to have strict eligibility criteria, of which the most common is "permanent academic position in a recognised higher institution", closely followed by the often unstated criterion "demonstrates experience and an established presence in the field, and is the most suitable permanent post academic to lead this particular proposal"
In other words, it is probably not possible for you to be writing a grant at this stage. Which means, your best bet of actually continuing this line of research that you're banking the rest of your entire career on, may in fact well be to convince someone grantworthy to apply for a grant on the basis of your ideas, for you to continue working with them. Otherwise, once you're out of the phd and looking for a job, your most likely route is that you'll have to join a project based on a grant that someone else proposed, which is unlikely to be your particular niche topic that you so love. And this doesn't even address the whole "even if you apply for a grant yourself to resurrect this line of research once you've made permanent, say, 7 years down the line, this research may no longer be grantable, based on current trends and buzzwords".
Having said that, there are ways for you to be an official contributor on the grant proposal, rather than simply be a person that your PI happens to hire with the grant money. Many funding bodies allow the concept of a "named researcher" on the grant. This is typically someone who is at a stage in their career that is ineligible to apply for the grant per se, but it is understood that they are an integral part of the proposal (typically understood to mean the project is largely their baby and they will be the ones pouring all the work on it), and is therefore named on the grant. This is great for your CV, because it shows you have experience submitting grants and getting funding. Plus it saves the university time and money because they won't have to go through the hiring process.
So if I were you, not only would I encourage your advisor to write the grant, but I would try to find out if you can be a named researcher on the grant and continue your research with them in that capacity.
Ok, I am lying a bit, because there is in fact another, more straightforward way to go about this after your phd, which is to apply for a postdoctoral fellowship. This is an award that allows you to work as a postdoc for a few years working alone on your own research. But at the end of the day, these grants are far rarer than traditional grants (which are already in high competition), and are thus even more competitive than normal grants, are much less flexible (e.g. in terms of creating a partnership), and still require finding an interested supervisor to supervise the work. If you do get one of these, it may be seen more favourably than a named researcher route (in that you won such a grant directly), I'm not too sure. But in reality, if you are a named researcher on a grant, this is already great, much easier, and will still allow you to control and continue your research.
These are all personal opinions, and I'm also still learning the ropes and shortcuts of the system, so I may be wrong on a couple of points. But more or less this has been my experience. Happy to be corrected in the comments below. Hope it helps.
PS. The cutting edge novel stuff I was working on during my PhD that I thought would change the world and I was ready to base my entire career on? Haven't managed to touch that in 7 years now. Now that I'm getting a permanent post I may go back to it, but I've already got other projects in my hands already, which are far more practical from a funding point of view.
* Though in practice, even here, I think you're probably underestimating the impact that your supervisor will have had, both in terms of what they contributed to the research in indirect terms, as well as how the impact of the paper may have changed from the network effect of having their name on it.