The problem is that most languages with exceptions treat that as the idiomatic error mechanism. So checked exceptions were invented, essentially, to do exactly what you say: add the exception type to the function signature.
Having separate errors-as-return-values and unwinding-for-emergencies is a much more recent trend (and, IMO, an obviously good development).
I should have stressed the "opinion" part of "IMO". What I mean is that, when I read this, it struck me immediately as being exactly correct: https://joeduffyblog.com/2016/02/07/the-error-model/