I think if you consult the literature you'll find that the prevailing trend is for markets to become more continuous rather than more discrete. Continuous markets help with true price discovery. Our markets are continuous in time right now and we've pretty much squeezed the spreads to their maximum, so while prices aren't continuous they are about as close as we can get w/o eliminating the profitability of the primary market participant (market makers) that make it function.
You can scheme up any number of possible microstructures that sound interesting on the surface. There's a reason why none exist. Remember, there is nothing to stop you from implementing a time-discretized market place. Current regulations (Reg-ATS) allow for you to do so. You'll find it hard to compete. Some markets do perform large scale discretization for block orders. Read up on POSIT and related ATSs and dark pools.
FYI - I wrote the successor to posit. Point in time matching goes out of fad when volatility increases. Why take on the risk of executing a block at a single point in time when you can spread that risk out over the day?
I read somewhere that non-hft tend to trade much more at the "second" tick. This may have been b/c they were dumb (hard to believe) or because converging at the same time (15:30:10 instead of 15:30:10.175) gives them better chances to finding a match to their sell/buy position
With insufficient trades, you cannot know if a certain price is really what the 'market' wants to pay, just what that one person at one point in time wanted to pay. Overgeneralized, the more trades, the more accurate the price gets.
You can scheme up any number of possible microstructures that sound interesting on the surface. There's a reason why none exist. Remember, there is nothing to stop you from implementing a time-discretized market place. Current regulations (Reg-ATS) allow for you to do so. You'll find it hard to compete. Some markets do perform large scale discretization for block orders. Read up on POSIT and related ATSs and dark pools.