It might be the "rational thing to do" but it's not a logical argument -- which is what makes it a fallacy.

Fallacies can often be the logical thing to do. E.g. an "Ad Hominem Fallacy" might save your ass when the other person puts forward a perfectly logical argument, but to serve their own selfish reasons to your detriment. An "Appeal to hypocrisy" can serve to highlight when the person you debate with wants you to stop doing something (because eg. they say its bad) but keeps for themselves the benefits of keeping doing to (and thus gets the upper hand on you). And so on.

Still, like those things "Appeal to authority" is not a logical proof based on the content under discussion (and axioms, logical steps etc), but a "because X says so" on the status of person X (eg. their expertise).

That's what makes it a fallacy. Whether what that person says is true or not, or even whether it's more likely true than not, is irrelevant.

In either case, it's not a logical proof (in the formal sense) nor a definite proof (the person with the expertise could for example be lying to further their interests, or mislead for some other reason).

I'm making the point that often times, appealing to authority is most likely to produce the correct answer.

That's true for most so-called fallacies. Instead they are evolutionary shortcuts to getting the correct answer (at least at evolutionary kind of situations).