There's nothing saying you can't keep the subject lit longer.
This heavily depends on the subject. Corals & stuff, sure, but anything mobile like a fish is likely to swim away when you shine a big floodlight in its direction. I shoot with a pair of Archon D36V LEDs, and this happens way too often - much as I loathe to part with the money, I see a pair of ST-100s in my future. Also, one of the main reasons of using artificial light is to overpower the green/blue tint of ambient lighting at depth, and a longer exposure will do nothing to help with that.