> Why can't I as a regular retail investor trade a stock on Saturday?

Because stock exchanges don't run themselves. There's all kinds of services with humans in the loop, and without these, you'd have a market with much less guardrails than the current public stock exchanges.

You can make a case for such a market being good or bad for society, but it currently simply wouldn't be legal in most countries.

> Why can't I move money from one bank account to another on Sunday?

You can in many countries! In the EU, SEPA Instant is going to be mandatory soon. In the US, I can already do this between two of my bank accounts; most banks unfortunately don't participate yet.

The larger problem seems to be that the US simply does not have customer-initiated account transfers (to third parties) in the first place. In a way, the reason why you can't do bank transfers on the weekends is that you can't even do them on weekdays either.