It gets a little complicated: do you want to continuously display market data and only clear trades once a second, effectively having a visible two-sided auction once a second? Or should it not be visible? (In which case you're no longer giving market data to all market participants, something they'd rather see)?

There are a couple of large firms that make 5-6 figures a day from arbitraging the closing cross. I'm sure they'd love to run their strategies all day; whether they would make more money than HFTs make now is anybody's guess.

Not if they couldn’t be processed in that time.

It is an interesting thought experiment though.. quantize time as well as price. You could exaggerate to one trade per day for the thought experiment. Now this would be on human scale so there is a lot of information that would build up (same when markets are closed). Between that and no time quantization like now, there are probably a few different positions (like electron orbitals) where positives and negatives vary quite a bit. Maybe one of them is better than the current system. Maybe not.

But.... Why?

What problem is this solving?

Seems like a lot of faff to get people worse prices.

I'm talking about all bids and asks being aggregated in the given window, and matched/executed at the end of it at once.

That would result in what was described above. You are taking unnecessary risk by committing to place an order at some point in the future. You might not be so sure a second from now.