>I've been in teams where pull requests that significantly cleaned up the code base were literally rejected, because people were paranoid that any change at all could break something in unforeseen ways.

That's why you need to surround the code with realistic integration tests first before changing anything.

>Ultimately, the only way to get yourself out of this hole, is by encouraging people to take risks

No, that's absolutely wrong. You need to first de-risk changes by creating a test harness that catches the bugs that terrify your developers.