Correct me if I'm wrong, but doesn't not picking a god give you a deserter penalty? The only place where this could happen should be co-op, no?
I'm not saying that should happen in co-op, but it feels a bit dishonest not to mention that.
As for the problem, maybe one solution would be that dodging co-op queues should stop you from queueing co-op specifically for a short period, as there are people who are just bored and go troll in the lobbies.