Would an optimization proof-of-work problem where the entity with the lowest hash wins have any security weakness or other disadvantage?
You're not thinking like an attacker yet. ;) 

Beside this incentivizing selfish mining, a miner can do the following attack:
Mallory sends all her funds to herself every block.
As soon as she finds a block with a very low hash, she can execute the following attack: Make a payment to someone that accepts first confirmation with a substantial fee ensuring it will be in the next block. Wait for the next block. Receive the counterside of the deal (e.g. coins on another chain). Publish their block and laugh.