Just a few questions/issues popping up on top of that:
Who and how would create a list of violent games?
How would one prevent you from playing such a game if you didn't pay?
Who would collect the extra money? Where would they go?
Why game developers would be okay with so much money going who knows where and not to them?
Why would game developers be okay with this at all, since violence is the basis of a good share of genres?
How would you monitor underground and small games?
What about browser and flash games located on the same site? How would you block access to ones without blocking the others? And even if you could block some smaller sites for even having 1 violent game, you can't pull this trick on facebook and such.
How would you qualify games with optional violence, such as salem? Implying that every person will use it's violent side if given an opportunity contradicts presumption of innocence.
Why bother with online gaming at all if people can keep playing games as and much more violent offline?
What does provider have to do with this? Why not just oblidge devs charge extra to skip a good bunch of extra steps?
Playerbase of most online games consists of people from all continents and dozens of different countries, how would that work out if, let's say, a good share of americans suddenly disappeared?
I realize there are some answers to those, but all the solutions I can think of seem either insanely complicated and not worthy of anyones time or easily avoidable.
As for internet costs, I'm paying 5,5$ total for ~100 channels cable + this:

So no, I wouldn't pay 25 more, there are plenty of other things to fill the void.