>or even "I sold some crypto" are unlikely to be sufficient answer to avoid your account being frozen

For 99% of banks, you'd be totally wrong about that.

> a note sent to the relevant authorities.

This, of course, means literally nothing. Banks will "send a note" for just about any reason. This results in said authorities drowning under a mountain of millions of pointless suspicious activity reports.

> If you deposit a quarter million dollars into your bank account out of the blue the bank are absolutely going to ask you where it came from,

I've deposited a larger lump sum into a US bank account and was never asked where it came from. I was then able to use that money the same day to pay off a loan.

What they actually tend to do is have someone in management call to congratulate you and invite you to discuss banking products. I know this from personal experience.

In the worst case your funds would be frozen for a couple months then you’d get a letter saying we are closing your account for compliance reasons and attached would be a cashiers check for the balance of your account. Then they’d file a SAR that would get put in a queue behind the millions of others because the government only reads a small fraction of them.