Further: Suppose you had an auction on shares once an hour, or even once a day, but no continuous trading. Would that make the world any worse off? (except for high frequency shops?)
I mean, what you're describing is how to create a black market in securities for people who want to act on news, knowledge, or sentiment before tomorrow's auction.
Sooner or later (spoiler alert: sooner) someone would put it on the Internet, and it would be unregulated, at least at first, and the insiders would do even better than they are now.
You should read up on the early days of ECNs, Island and Archipelago and what not. Alternatively, you could look at this exact script being played out in crypto right now.
I doubt it. I've never heard a coherent explanation how liquidity on sub-second scale is a great social good, while at the same time the largest equity markets in the world are closed 2/3rd of the day, plus all weekends and holidays.
Because real world information has sub-second resolution and a healthy market should reflect that. It’s a continuous auction. Some markets are open longer such as FX.
The NYSE is closed between 16:00 and 9:30, plus all weekends and bank holidays. AFAICT real world information doesn't stop in the closed hours. So how is it credible that it's super valuable that trades can happen during the open hours at sub-second resolution, but we're suddenly ok at 16:00 with a 17.5 hour resolution?
You are begging the question. Why should a market reflect that? Why is that preferable to a daily auction (throw in a stochastic cut-off time to thwart HFT even more)?
Because you can’t make sure that all auctions happen at the same time. Consequently, news will disproportionately affect stocks having an earlier auction. That’s just one reason I’m mentioning.