From what I can see, the "best price" rule basically becomes meaningless in the face of HFT. Alice is pretty much always going to get her min only, right? This prevents Alice from setting her min lower to manage risk. e.g. In a world where matches are executed immediately, but market makers are competing without an advantage, Alice could set her min at $9.50. If Bob comes along and buys at $10.05, great. If Chuck comes along at $9.55, not as great, but okay. But in a world where HFT will pop up and buy at the lowest possible price, setting a low min stops being a reasonable option, because you're basically capping your sales price at that point. So maybe HFT helps Alice get $10 instead of risking $9.55, but it also stops her from getting $10.05.
I know that market making could theoretically do this anyway, but it's a different situation when market makers have such a speed advantage. If you've got to sit on your position as long as the typical eTrade user, leaving a passive buy for $0.10 under market price picks up more risk, because you might not be able to cancel if the market shifts downward by $0.30.
You're using terms like "best price rule" but asking questions like "if Alice sets her 'min' at 9.50 she can sell to Bob at 10.05". This doesn't make sense. Alice has a limit order on the book that says she's prepared to sell at 10.00. When Bob comes along saying he'll buy at 10.05, the market fills the order at 10.00.
There are some things I'm not entirely clear about here. I'm not sure how the best execution rule (best price rule is apparently a bit different) plays out when there's a spread. When someone bids 10.10 and someone else asks 10.00, how should that be resolved. Either someone takes the whole spread or it's split between them, and I'm not sure what the SEC says should happen. A "minimum" price doesn't make any sense if it's the only price, but then neither does a "maximum" price.
In any case, though, the spread would theoretically go to the existing participants, rather that an HFT. The "market making" of the HFT still results in extracting money from the market. This could be a beneficial thing in illiquid markets, but I'm not sure it's beneficial in markets that already have high liquidity.
You're not clear on how order books work, which, respectfully, suggests that your reasoning on this stuff is a bit suspect. The standing limit order prices the trade.
I can understand how upsetting HFT must have sounded to you (although to be fair, we're still shifting the good outcome from Bob to Alice in your best case) given that misunderstanding, but, no: to capture the 5 cents (more likely: 1 cent) between Alice and Bob, the HFT had to accept Alice's downside risk exposure. There was no (simple) outcome where Alice could have it both ways, scalping Bob for 5 cents in the best case but getting out at 10 cents in the worst.
I came to my understanding of this topic in a weird way (see downthread) but one resource I found extremely helpful was Larry Harris' _Trading And Exchanges: Market Microstructure For Practitioners_. It is the TCP/IP Illustrated of markets. Very well written, and well written in a way easily appreciated by programmers. Highly recommended. When I first started reading it, I literally didn't want to put the book down.
Respectfully, I never claimed to be an expert of any sort, and I said so earlier. A large part of why I participate in these kinds of discussions is so I can learn.
I still get the feeling that you think I'm attacking HFT. It's not "upsetting" to me. The only questions for me are whether there's more value in HFT than cost, and whether the same value could be had with lower cost. It's good to know that my Alice scenario is invalid, though. That means HFT isn't breaking what I thought was a useful scenario for sellers.
Thanks for the book recommendation. I've added it to my list.
I know that market making could theoretically do this anyway, but it's a different situation when market makers have such a speed advantage. If you've got to sit on your position as long as the typical eTrade user, leaving a passive buy for $0.10 under market price picks up more risk, because you might not be able to cancel if the market shifts downward by $0.30.