The problem with automap being always visible is that it distracts the player from navigating based on the actual game world.
It took me a while to realize this but once I was aware of it, it became even more distracting and tiring: My eyes are constantly scanning between the center of the screen and the upper right corner of the screen.
As I am playing Diablo 1, 2 and 3 quite often these days I can only verify that this does not happening in Diablo 1 & 2 and I feel much more immersed to the game world because I am actually focusing on the sorroundings of my character while navigating and only occasionally popping up the map when I get lost. Even in these cases the maps in the first two games are nearly not as distracting as the map or the automap in D3.
If complete hiding is not possible, an option to increase the opacity could also help a lot.