The general consensus at this point is - no one actually knows - and it's up for serious debate. We know lack of liquidity absolutely has negative effects (because we've experienced it), but we don't how much liquidity is "too much".
One day we may decide to turn that knob from the millisecond range to 1 second and see what happens. If it's bad, we can always turn the knob back.
It's not necessarily clear whether it could be reduced to seconds of liquidity, or minutes, but it's clear that milliseconds is too short. The money isn't remaining in the market long enough to provide value -- especially when the market has already been made and they're just trying to figure out who gets the surplus between ask and bid.
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.
However, you postulate that the introduction of a turn-based system would effectively transfer money from Joe Sixpack (who'd face higher costs) to hotshot hedge fund manager (who'd face even lower costs).
Maybe, though, we'd see HFT shops go out of business (and not building micro wave towers between Chicago and NY anymore), and see a transfer from HFT shops to hotshot hedge fund manager and Joe Sixpack, both facing lower costs.
How do you know it's not this second scenario?
These systems are already running in many markets, typically at a rate of one trade round per day, but using them is optional.
Once you disregard the rapid transactions that do not have a significant effect on the price, your average human investor is probably putting down some fill-or-kills or limit orders and actually benefits from HF liquidity trading.
It's hard for me to understand, let alone explain, why milliseconds would matter for the human investor, but I what I can tell you is that GS is not investing 100M USD just for buying derivatives every other minute.
If a security could only be traded once per 10 years then it's obvious that its lack of liquidity would make it less valuable. Holding it would tie up your capital quite significantly.
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.
It seems to me that a model where traders all compete for how many nanoseconds away their HFT servers are from the action doesn't really benefit the market as a whole. If anything it just makes things like flash crashes more likely.