I know some password managers (myki, lastpass and I think 1Password have an option to toggle it off).

It's on by default, which should be true for most apps with confidential data. But other apps (like photos and messaging apps, can at least have that as an option defaulted to false, for users who would like the extra privacy)

Yeah, for some reason web browsers feel the need to do that when browsing in private mode.

It is one thing to block automatic screenshots or screen recordings. Another when the user explicitly tries to take a screenshot.

I imagine the reasoning is that if you can do it, some other app might be able to trigger it, and at that point, it's all downhill.

It's an OS function triggered by a physical button. If some other app can imitate that then surely it is already game over?