Right? Why do we even need all-day trading?

I have seen a once-daily auction proposed, which seems like a sensible approach to me.

That wouldn't be enough liquidity, and also wouldn't solve the problem if the auction happened at a specific time. Day traders would all put in their bid at the last possible moment.

What solves the day trading problem is doing chunked actions at random small intervals (like between 2-7 seconds). Then you can't put your bid in at the last moment because you won't know when it is. So your best bet is to put in your bid when you've chosen a price, knowing that it will resolve within seven seconds or less.