^ You are basically saying that what I am calling for has already happened, except that Marvel doesn't have the balls to go all the way with it and put the X-men in their own universe separate from 616. They are stuck in limbo, and I think Marvel needs to make up their mind where they stand on it. Also, I don't really agree with your suggestion that getting powers through an accident is like winning the lottery. Peter Parker is just as much of a "freak" as the mutants, but he's not seen that way simply because he wasn't born like that. If people are going to have animosity towards mutants, the realistic thing would be that it spills over into animosity towards everyone with superpowers. But then of course, the uniqueness of mutants being born with their powers disappears, because it becomes little more than an easy explanation for people having powers.
I think that the best solution is to simply have one universe where everyone gets their powers from technology, magic, and science accidents (616) and one where they get their powers from mutations at birth (X-men universe). It would solve pretty much all of the problems that have been brought up, and the only problems it would really create is that there would be a lot of retconning needed, and some of the kids would have to be split up in the divorce (i.e. do the mutants who are more associated with the Avengers stay in 616 and get new explanations for their powers, or go to the X-men universe?). Also, there wouldn't be crossover stories between the X-men and non-mutant superheroes anymore, but honestly I could live quite comfortably without that.