Are there advantages to having more than one private key per wallet?
Well, you don't really want one private key per wallet, you want one private key per transaction (and this is what the default client does anyway).

But you may want to have more than one wallet, because otherwise you might be mixing "accounts" that you want to keep separate: If a single transaction output is not enough for a given payment, the default client will use multiple, and that way your otherwise unrelated "accounts" become connected.