> And yeah, under my system market making actually requires work/risk, not just riskless front running. The free lunch is gone. That is the point. There would be less volume. Buyers and sellers would trade slightly slower trade execution (waiting for the auction interval) for the benefit of not paying any tax to market makers.

The spread earned by market makers is definitely not a tax. They earn the money from (increased volume * reduced spread). Suppose you anticipate AAPL will rise from $600 to $601 based on your fundamental/technical analysis. If there're no market makers, the wouldn't be enough liquidity to inspire any confidence to take the trade. The order book would be like:

601.00 3
600.50 1
5 600.00
2 599.00

There's no point to make that $1. It's simply too risky. If there are a buyer and a seller they both want to trade 1 share instantly. They pay $0.50 in total to liquidity providers in the market (compared to private settling).

If there are lots of market makers, the order book would look like this:

600.10 950
600.05 401
1200 600.00
450 599.95

Of course, you will choose to trade and make the $1 if market moves as expected (and a lot of people will make similar decisions). At this time, if a buyer and a seller comes, they will pay $0.05 in total to market makers compared to private settling.

I know that your original intent is to make the "private settling" option available in the market by aggregating all orders in an interval and execute at once. If that really happens, the order book (which is hidden from public) will look like this:

600.50 2
600.00 3
5 601.00
2 600.00

Execution price: $600.60 (Weighted average of overlapping orders). Volume: 5 shares.

In this case, it seems that both the buyer and the seller received a benefit. But actually it's not true. If your aim is to make profit by selling at $601, rationally you will keep buying until the price reaches $601. The maximum price you're willing to pay is actually $601. However, when you see a selling order at $600, you will place a $600 buy order instead (and you pretend to have a demand only at $600 or below because you know it will be fulfilled anyway). In a non-continuous system, you're forced to signal your true demand at $601 so that you are able to take advantage of favourable prices when you're lucky (and orders get executed only when you're lucky).

> If the market was as jump and irrational as you think it would be hedge funds would make a killing by being smart and rational, until enough entered the market with standing limit orders that the price smoothed out.

They are exactly market makers. The market will be "jump and irrational" without these market makers, especially when everyone signals their true demand. That's why black-box auctions usually yield much higher prices than public auctions when people are rational (i.e. not counting the emotional effects of public bidding). It's just how market works. Similar concepts can apply to free rider problem as well (for public goods). You know that the national military can provide you security worth $1,000 a year, but obviously you pretend to be unwilling to pay anything when the service can only be provided for free. Market equilibrium price quickly reaches $0 with no guess work.

The way market works makes the prices very predictable. Even the flash crashes are smooth (with the market makers). The "riskless front running" is a symbol of market competition. Yes, some guys are going to offer you one cent better, they should have the priority in the queue.

I don't want to comment on the influence in economic activity. What I know is, more liquidity = less risk for holding shares. What market makers earn is not a tax. It comes from the money that bigger market makers will earn anyway ($0.01 spread with 50 shares traded vs $0.50 spread with 1 share traded).