... Refinements could be that X transactions below Y BTC don't require confirmation and are paid from the "hot" wallet or similar.
Yeah, Bitcoinica did do that. it was their hot wallet that got cleaned out.
Considering that they had over 40,000 BTC in their "hot" wallet, it doesn't look like they were limiting it to small transactions.
Consider the way this would work at a brick-and-mortar bank. The bank needs to be able to handle large withdrawals, but it doesn't start out each day with $10,000 in every teller's register. Small withdrawals can be handled at the register, but large ones require access to the safe, which comes with some extra oversight.