> However, if you had a turn-based market where every trade got cleared at the top of the minute it's not clear to me at all whether that would effectively be less liquid than what we have now.
The primary problem with that is that it pools order flow into a homogenous, undistinguished pool.
HFT heavily rely on profiling order flow into the informed and uninformed. A typical uninformed trader is Joe Sixpack who's rebalancing his 401k. A typical informed trader is a hotshot hedge fund manager, who's invested enormous resources in gaining an informational edge. If Joe's buying a stock that doesn't tell you anything about the value of the stock. If hotshot hedge fund manager is buying a stock, that in and of itself is a credible signal that the stock's worth more than you thought it was.
Liquidity providers love being the counterparts to Joe, and hate being on the other side of the hotshot hedge fund managers. The more you can profile the order flow, the better prices and more liquidity you can offer to Joe, by charging the hotshots more. Think of how life insurance companies can offer better premiums, particularly to the healthy, if they require a physical exam before underwriting a policy.
Even on a millisecond by millisecond basis, there's a ton of distinguishing characteristics regarding the informational content of order flow. Uninformed flow basically looks like a bunch of small, randomly spaced trades. Informed flow is more likely to cluster together in small time windows, move sequentially in the same direction, try to sweep liquidity with huge trades, and immediately follow similar moves in other securities among other things.
If you pool all orders into a homogenous one minute pool, HFTs would lose much of their ability to segment order flow. The end result would mean that the hotshot hedge fund manager would see his trading costs reduced, and Joe Sixpack would see his trading costs increase.