That's effectively time-based request sharding which seems sensible but you'd still have to reconcile trades and any open positions (etc) across the time boundary where one system stops accepting requests and the other one starts. And keep the databases synchronous (ie have some system to make sure they're in sync at the changeover time) - or have a few minutes/hours of downtime between weekends and weekdays while you copy the whole production database from one system to another. The devil is in the details!
For what it’s worth, in some financial markets, there is a sort of natural daily cutover time [0] across which you are often not trading quite the same instrument. For example, the settlement date may roll over, etc. And a lot of Very Serious Finance is already built on the idea that most parties do not instantaneously reconcile anything and don’t depend on real-time trade lists.
I really can imagine a system in which the Monday trading system runs all day and then turns off at a predetermined time. Then it has 15 minutes to produce and disseminate a final list of all transactions, after which it becomes completely unavailable and is ready for maintenance. Any subsequent amendment to Monday’s trading would be done out of band. Open orders at the end of Monday do not carry over immediately to Tuesday, although front ends are welcome to recreate them. Everyone would understand that liquidity would be thin for the first few seconds after the system rolls over.
For added fun, Monday and Tuesday could actually be allowed to overlap in a hypothetical trading system, although the market participants might not love this.
[0] which is not the same for all instruments, and holidays mean that not every instrument rolls over meaningfully every day.