What is the advantage of such a market? Near as I can tell, what would happen is that whenever the market believes the price should move, liquidity will drop to 0. Eventually the market will allow trades at the right price, and liquidity will return. Why is this a good thing?

Also, HFTs will still exist. Suppose the "right price" is $50 - even if the market hasn't adjusted (say it's stuck at $51), HFTs will race to have their orders first in the queue at $50 for when the market does readjust.