Attempts at doing this are effectively already existing, the IEX [1] exchange being an example, albeit on a less ambitious scale than your idea:
> It's a simple technology: 38 miles of coiled cable that incoming orders and messages must traverse before arriving at the exchange’s matching engine. This physical distance results in a 350-microsecond delay, giving the exchange time to take in market data from other venues—which is not delayed—and update prices before executing trades
IntelligentCross Midpoint (a darkpool) is a better example, since it actually does matching periodically every couple of milliseconds [1]. IEX just introduces additional latency for everyone.
I suspect this would put everyone on more even footing, with less focus on beating causality and light lag, placing more focus on using the acquired information to make longer-term decisions. This would open things up to anyone with a computer and a disposable income, though it would disappoint anyone in the high-frequency trading field.
Imagine that a company announces the approval of its new vaccine a few milliseconds before the periodic trade occurs. As an HFT firm, you have the technology to enter, cancel, or modify your orders before the periodic auction takes place, while less sophisticated players remain oblivious to what just happened. The same applies to price movements on venues trading the same instrument, its derivatives, or even correlated assets in different parts of the world.
On the other hand, you risk increasing price volatility (especially in cases where there is an imbalance between buyers and sellers during the periodic auction) and making markets less liquid.