I think the noidea idea was quite good, but quite possibly what struck me as the worst thing about it was the philosophy it implied "oh you don't need an idea to be an entrepreneur, just start a company anywayy!lol". I know that's not the whole truth of it and that many people wind up changing their idea, but that's the feeling it gave me (and I feel many others).
Out of curiosity, what makes you think that managing YC is n^2? Certainly everyone would need to communicate with you -- that's n. The question is whether or not each YC pair would need to communicate with each other. That is n^2 and seems like an excessively high level of message passing.
Human memory is not linear. The difference between having 10 teams and having to remember their names and their ideas and their challenges and remembering 20 teams is more than a 2x increase in difficulty.
In its then form, every partner had to know what every startup was doing, and the number of partners was a function of the number of startups.
So n log n.
The number of partners you need is not the log of the number of startups. It's more like n/15.