Artful Dodger & others: From my experience, playing 500 games and staying ahead of things takes about 4-8 hours playing time a day. Every day.
Of course that depends a bit on how much you think about each move, but it doesn't get much faster than that.
I have managed to play 1400 games for a month or two, but it took its toll on my work live, and I got a yellow card from my wife. So now I'm working to get it down to less than 250, which will be nicely doable in the evening hours.

I think there should be a limit for everybody (no matter what membership level), for example to not be able to have more than 500 games running, until you have more than 400 running for a month without timeouts, etc. If you can handle, the limit goes up. If you time out, the limit goes down again.

But maybe it just takes a grown-up mind to control yourself. And a lot of players are not grown up, and behave like a kid in the candy store. We all know how that ends...