You can be scammed into entering your password into a random textbox and then relayed on the actual website/app. This is too basic. In case of FaceID/TouchID, the acquiring platform (your mobile phone) has secure device binding and FaceID/TouchID is a local authenticator on that device to use that secure device binding to authenticate. If FaceID/TouchID becomes fakeable, we will move on to some other more secure local authenticator. The point is, you have a rich multi-sensor mobile device as your authenticator.

> Also sometimes I need to change them (if they get compromised, if computing progress made them easier to bruteforce, etc.), and I don't really want to have to use cosmetic surgery when that happens.

That's not how it works. Each hardware device that acquires your FaceID or TouchID (or Iris ID etc) do it in a way that's unique to them. Even mission impossible style face mask can't fool these modern FaceIDs. Like all things in security, it is a game of making it really expensive to break it and not really about it being impossible.