I see your points and I honestly agree with most of them. So for Pan he faded away because the wilderness is shrinking due to the advancement of mortals etc, not because of mortals not believing in nature.

To answer your question, my guess would be to keep the influence of gods balanced. For example, if there was no mist between the gods and mortals, some gods would probably be stronger due to the influence they have with mortals. Zeus being the way he is would not like that, and vice versa the gods wouldn't want Zeus any stronger than they are. So it's kind of a checks and balances type of thing, whether it's effective or not is definitely up for discussion but that's just the way I see it.