I think people should be able to pay to play as many games as they like. Lack deserves to get some cash for this site while still keeping it free. Money could go to server costs with leftovers going to Lack's pocket.
The site is growing. We used to have 10 games in one go and only 30 members (Three days after release), but now after about two months we've got >1000 members and only 4 games. The site is brilliant. If people pay then there can be more server space and more updates and such.
The only downside I can see is that paying people might feel angry that non-paying people are still getting stuff although they give nothing and that non-paying people might demand more games since the paying people have them. This is of course stupid and irrational but that's how people go.
So Lack, go ahead and put in a pay for more games option, I'd sure love more games and they'd definitely be worth more to me than the french fries and soft drinks I'm currently spending my spare cash on.