This would work for some amount of time. However, foreign banks are unlikely to hold USD-type value without a correspondent banking relationship or a custodial banking relationship exposed to the US market (and hence US regulation).

The reason many, especially smaller, banks don't want to do business with criminals is they fear they'd lose their access to the US market through a termination of these relationships. This would then push the bank into insolvency.

I know this because all this happened to Tether, lol. There's been some documentation, likely as part of the NYAG lawsuit or the Paradise Papers leak -- or both. Noble initially refused to bank them for this reason, so they invested in Noble, who then took them on as customers. Their custodial bank (Wells, IIRC) told them to eat dirt, and it pushed Noble into insolvency.

Well that’s precisely why we have all these customer onboarding / AML regulations. To onboard trading clients (think hedge fund) I’ve seen compliance ask for corporate structure diagrams, lists of the major shareholders with bios, list of the board of directors, articles of incorporation, addresses, copies of the counterparty’s AML policy, etc.