I had the "please tell us where your money comes from" message and my app continued working just fine (I use Revolut for all my personal transactions). Once I sent them a copy of my bank statement and some invoices between my company and me, they restored full access to my account super quickly.

While those things could be true, as a N26 and Revolut free customer, I have to say that yes, they use customer service chat bots, but when you ask for humans, their assistance to me was always good, quick, and solved my issues.

I was on Premium when my account was frozen ;-)

And I did ask for humans, on 3 separate days, as I said, took about 10 days to get a reply.

You're not talking to support when your account gets locked, you're talking to compliance. And it takes time due to same reason Monzo has talked about:

https://monzo.com/blog/2019/10/18/watchdog-response

Did they give any explanation as to why they think that's legal, freezing accounts and blocking payments on a whim, without some court's decision?

AML/KYC laws require you to freeze accounts if you suspect anything.

Traditional banks blocked my transfers a few times and required proof of source.

When Revolut first launched in Singapore, it was almost common knowledge that depositing more than $5,000 SGD (approximately $3,500 USD) would more or less cause one's account to be limited for weeks (until one tweets at them to hurry up), because they've triggered the Source of Funds check.

Did you do anything "weird" or was it just during your average months that they suddenly went ballistic?

I know they're supposed to alert the authorities on suspicious activity, but I believe(d) freezing an account unilaterally is the ultima ratio for extreme cases and wouldn't be done easily, as it will leave the bank open for damages claims, and really makes banks somewhat useless if it happens frequently.