Oh, I see. But I suppose on a Pixel 4a you could configure both face unlock and the fingerprint scanner and thus get best of both worlds. I personally don't find touching the scanner to be a nuisance for case #2 since its location on a Pixel 2 or 4a's chassis is such that you can do it without fiddling with how you hold your phone (your index finger tends to be near the scanner during phone use, whether one- or two-handed, anyway).

Ok, but interactions of type #2 are probably a hundred time rarer. Personally, I rather like that I have to actively decide to authorize the use of a password.

Yeah, #2 could probably be abused by a malicious app.