It depends on your definition of "overdone". Has it been done A LOT? Well hell yes. But so has sci-fi, military shooters, platformers, sandbox games, simulators, horror games etc etc etc. Gaming is such a huge and diverse buisness now that one cant simply look at the number of one genre, notice its fairly big and go "oh my, so many titles, it must've been overdone". It would be like trying to count individual rice grains in a basket and claim "yep, overdone".
If the demand is there, it's there. And since many zombie games keep selling like butter, it clearly hasnt overreached its demand. So if the definition you're looking for is: "Has zombie games been overproduced beyond demand?" then the simple answer is no.
Could it be more diverse? Naturally, but I'd like to think diverse zombie titles have been coming out lately that are taking a relativly new take on the whole zombie apocalypse setting.(TWD and dayZ to mention a few.)
Why zombie games are so popular is a different question entirely. I guess it's a mix with the action it usually involves, our chance to slaughter hordes of humans that arent really humans(and thus we dont have to feel bad for it), the sudden rise in interest in apocalyptical themes(global warming and whatnot raising our awareness of our own fragility etc) and the huge potential for different survivor tales that can be crafted from a zombie apocalypse setting.
Is this going away anytime soon? I dont think so, I dont think its even remotely likely. Its not going away until the demand starts to diminish, and as long as games like The walking dead, DayZ, State of Decay, project zomboid and Left4dead keep being released and appeal(and sell) to such a wide audience with their various tastes and priorities, the zombies are here to stay.