I have worked in a few high profile research institutes for my PhD and postdoc, and find myself a little intimidated by the "strong opinions" and arguments that seem to crop up at the principal investigator level. My personality is somewhat more laid back or agreeable, and I find myself wondering if this would be seen as a "personality flaw" in the somewhat cutthroat funding and scientific world (or at least that part I am exposed to). I'm sure it helps to have a strong opinion of one's own work, but I sometimes find it hard to do so, as I tend to be more self-critical and more concerned about stating something correctly and figuring out what is "right" than necessarily being self-promoting and overconfident in my own abilities, but I feel like that ends up manifesting as some sort of fundamental flaw in relation to others I see advancing into the faculty ranks.
I think a "big ego", or at least a healthy dose of self confidence, is necessary for survival as an academic. Our jobs are one of repeated failure. Success rates on grants, publications, experiments, and job applications are often less than 10%. In the face of such frequent failures an abundance of confidence is a require for maintaining ones sanity. Further, many departments verge on dysfunctional and there is generally someone looking to push you down to get ahead (I am not saying everyone is out to get you, but there is generally at least one person in every department looking to get ahead at your expense.) Being confident, outspoken and to an extent self prompting is useful for dealing with these people. The difficult part is not being too self confident and too outspoken and being able to admit when you are wrong.
It's important to distinguish inner from outer perspectives here. Someone that is perceived as 'having a big ego' might not feel that way inside, and might be compensating for a bad case of Imposter Syndrome. Or they just might have a big ego through and through :).
As others have pointed out, what you really need is a thick skin, in order to deal with the constant rejection you'll face (jobs, papers, grants, awards, ...). You can acquire a thick skin by having a big ego ("People are too stupid to appreciate my genius") or by being bull-headed ("I don't care what people think: I think this is interesting"), or by other coping mechanisms. This is an internal focus: it doesn't matter what you show on the outside.
Occasionally though, it's helpful to project an aura of confidence and assuredness, most commonly when you're interviewing, or when you're psyching yourself to write a grant or pitch a project. Again, this is an external focus: it doesn't matter how you feel on the inside.
Ultimately, you'll (hopefully) find a harmonious balance between what you project to the outside world, and how you feel on the inside. They don't have to necessarily be the same view though: they rarely are.
I am sure a psychologist could provide an indepth analysis to a large part of this question. I am not a psychologist so I will try to stick to what I think I can answer. First, it is usually the big and loud heads that stick out and are seen, there are probably just as many quieter academics in similar positions that you do not see or hear.
I am sure it is possible to talk yourself into a top position but not without showing excellence in your science, usually reflected in a publication record and funding success (sadly to a lesser extent teaching). But, the academic record on paper is typically what counts and it would only be in an interview situation between two equally talented candidates that things can be swung. But even then, I do not think the ego would necessarily have an advantage. Then there is the question what happens after you are employed and how one develops as a person but that is out of scope for me.
A problem more timid persons experience is to strike the right tone in pushing ones own merits. Taking advice from entrusted clleagues is a good way forward. But, as a whole a "big ego" in the negative sense is not necessary, a good academic record is.
A "big ego" is definitely not necessary. Of all the scholars I have interacted with, the biggest-shots were often less egotistical than the average person. Especially at the highest levels of academia, the strongest work often comes from those who are willing and able to listen to and improve on the ideas of others.
However, you do need to make yourself heard. You do need to be bold. I do not know a single successful tenure-track person who sits on ideas until they are sure that they're right. You don't find out an idea is right by mulling it over. You find out by formulating the problem rigorously, by testing a hypothesis, and by subjecting it to the most scathing peer-review you can find (not necessarily in that order, as you might do some of these steps multiple times). There's no harm in being self-critical or unsure that you're right. There is harm when that hinders you from taking the necessary steps to find out if you're right.
You don't need an ego. In fact, ego just makes life more difficult in many ways. All you need is to able to project confidence, and the ability to assert yourself. A simple ability to stand your ground and stand behind your opinions, even if quietly so.
Think about the guy or gal you know who doesn't talk too loudly but everyone listens when he or she speaks. Try to emulate that person, not the egos in the room. People generally dislike people with big egos, but they love people with genuine confidence. People will respect the hell out of you for it.
There are many resources online regarding how to project confidence--I suggest looking there.
Academia, as many other fields, is the survival of the fittest game. If you see PIs with big egos (or rather if most of the PIs you see have big egos), then it means that this is the personality trait that academia cultivates, albeit unknowingly, implicitly and subversively.
Academia is a race against time -- if you hesitate about your research idea for too long, and wait to perfect it, you will either be scooped, or will run out of your time in your (presumably rather junior) position. Submitting something that is just "good enough not to disgust the three referees" that you yourself know isn't the greatest paper, and getting it published, gets you the confirmation of "Aha, I am a smart enough person to game the system". Then you learn to salami-slice it to boost your # of publications; then you learn to attribute collaborative teamwork to yourself when your chair asks you, "How many papers have you published this year?" -- all these things sound a lot like "I, me, myself", and occasional big carrots (your R01 grant; your tenure) are obviously about you. When you do this for 20 years in a row, your skin gets so thick that it looks very much like a big ego from outside.
Don't worry, you will see big egos in most other fields at the higher levels -- think real estate development and golf, which are closely intertwined, anyway; you would not find folks in these lines of work very approachable.