It might depend a little on the fund but I think it’s probably right that conditional on a client investing a small amount of money, they are more likely a big pain to deal with. On the other hand I think startups often accept pretty tiny (eg 5-10k) angel investments. But maybe I’m wrong about that.

I think a typical hedge fund won't accept less than $100k. For a lot of brand-name funds, the minimum is $1M or higher. Many of them won't accept new investors at all, or when they do, it's for very large amounts of money. For example, Citadel is $10m+. Millenium is $25m+.