The problem with having computer separation be less than pilot separation is, what happens if the computers fail and the pilots have to take over? Then they're suddenly in a situation where they're already below whatever the minimum safe pilot separation is, and now you've potentially turned a recoverable failure into an unrecoverable one. If the whole point of having pilots is to be backups for the computers, the computer situation has to have more margin than the equivalent pilot one, even if efficiency is being left on the table.
(The only way around this is to not have pilots as backup, and turn the whole thing over to the computers, but we're not ready or willing to take that step yet)