Or other way around - in bigcorp (or in startup) choosing what to work on have much bigger impact than the work you do.

On very low level it's up to your manager. As time goes, even as IC you have a lot of agency. It's not just company selection, team selection, but also which part of the project you are working on and how you are approaching solving it.

Of course "if everyone does this, who will fix the bugs". However, the quickest promoted people I've seen are the people who were excellent at politics-izing (and sometimes foresight) the best work assigned to them.