And we couldn't spread ourselves too thin with introductions, because the supply of those is not even limited. Later stage investors are delighted to hear about any good startup we can send them. If we send an investor twice as many good deals, they're twice as happy.
Are office hours a good measure of advice? What about the dinners?
Is the advice really completely stateless?
Some of the benefit of YC comes from networking between the teams. I think this benefit may diminish as the group grows.
Just thinking up objections.
It's funny you should use the word stateless, though, because one of my tricks for scaling is to keep all the state on the client. E.g. I tell the startup "remember to tell me x next time we talk." I've been doing that for a while, and it seems to work fine.
Networking between the startups has actually increased. The more startups there are, the more likely you are to be in the same batch with another one that would be a natural beta user for your product, or that happens to be expert in some technology you have questions about. Maybe there would be problems with startups connecting if there were 1000 in every batch, but between 8 (summer 05) and 26 (summer 09) things just get better.
I remember 'stateless' from last year's 'Be Good' startup school talk.