There are ways of providing market makers without quite as much waste as the existing system of HFT. For example, instead of having the first trade order to arrive win, group them into generations of, say, one second, and execute them in a deterministic* order that does not depend on the time of submission (provided the trades arrived within the one-second window). You can still provide liquidity via automation, but you get rid of the latency arms race by providing a floor, below which improving reaction times doesn't win you anything.

* - For fairness, you could execute trades within a generation in a pseudorandom order determined by a random key, which is cryptographically committed to prior to the opening of trading, then reveal the key after the market closes to prove that you executed them in the correct order.

There are some big problems with that plan. If I want to sell 100 shares, but I think that you also want to sell 100 shares but there is only 150 shares of demand then I'm incented to put in an order to sell 200 shares so that I capture 2/3rds of the demand.

But you're incented to do the same thing! So if you're going to put in an order for 200 maybe I should put in an order for 400? You can see where this is going...

People worry about HFT destabilizing the market. It seems to me that would be a much greater risk if you're incentivizing people to put in crazy orders that they don't actually want to do just to grab the percentage of demand that they desire.

What happens if we aggregate both the supply and demand over a second (and don't allow price resolution smaller than a cent), then each seller gets to sell a portion of the demand proportional to the amount of this stock he owns?

This seems to disincentivize putting up for sale more than the seller wants to sell, and to also disincentivize "Sybil attacks" where the seller has an incentive to create false identities for himself. (Just a thought experiment, would be happy to know what I'm missing here :-)