You're not allowing it to, because your proposal quantized the market! That's what it means to batch trades and execute them at an interval: the price can't change inside that interval.
How? In every quantized unit of time everyone would be treated equally. If there is more demand than supply the prices goes up until there is not more demand than supply. This is also not even taking into account orders having ranges acceptable prices, which would add much more flexibility and granularity without needing more temporal resolution.
I don't think you've thought this through very carefully. Most orders in the market aren't "market orders"; they specify a price. Meanwhile, assume you resolve pricing in an automated auction: there's a spectrum of prices. Who gets the better prices?
If prices are given as a floor for selling and ceiling for buying they can be fit in a fair and methodical way through many different methods with any remainder being left over for the next tick. I'm surprised it is even such a controversial idea that a fair and fluid exchange can be made without resorting to a first come first serve structure.