Introvert here as well. Was promoted through the ranks to VP levels in spite of this. From management's perspective, sometimes it's not just picking the team that gets their specific work done. It's picking the team that you want to work with. Good managers will find a good balance for this. Bad managers turn it into a fucking sewing circle.

Consider their perspective: Do I want to spend 40 hours a week working with a brilliant fucking asshole, or the somewhat less capable person who doesn't make everyone else on the team want to quit?

Good managers will consider the perspectives of the folks they oversee; far too many managers are there because they're tall, have good hair, and are good at kissing ass and not much else. While, yes, business is business, that doesn't mean there isn't merit in figuring out how to make yourself into someone other people want to work with.

If the personal cost of doing so is too stressful or something you just don't want to do there's nothing wrong with that, but on the flip side, there's certainly a cost to it, unless you find a really good niche with managers who understand you get the best work out of people by putting them where they'll succeed.