I don't think there are any 'rules' when considering cover bands. There is one cover band near where I live, around Lemont, full of middle-aged fogies that play classic rock covers, and they aren't very good at all.
Then again, there are blues bands up in Wisconsin bar scenes that do mostly if not all covers of blues/blues-rock, and they kick ass. Great guitar players, great drummers, great bassists. They obviously play to the tastes of their crowds, but I've never had the impression that they didn't want to be playing the songs they choose to play.
I think it all depends. I think the only rule is that better musicians will attract other quality musicians and put on a better show than mediocre musicians, who will only attract other mediocre musicians and put on a not-so-great show. I think that's as true for originals bands as it is cover bands.
A better cover band will make the songs they play "theirs" and be more entertaining for a crowd while also keeping themselves engaged and interested in the songs. And, as a side-note, I tend to find that blues cover bands are often much more enthusiastic than classic rock cover bands.