Result will be like we see in Russia: deals between US businesses will become deals between their offshores, and just enough money to pay salaries, will be moved into the country.
Keeping money offshore doesn't make sense for the little guy. You're required to report it with significant penalties for non-compliance, and the anti-tax-deferral rules for controlled foreign corporations basically make repatriating just enough money to pay salaries a pointless exercise.
Since BTC, ETH, etc. are public ledgers, you're basically already giving every government agency in the world the ability to track your balances and transactions without any additional regulation or infrastructure required. Of course, if you're super careful, they might not know it's you yet, but if they really want to, they can find out and make sure you don't sleep very well at night while they wait.
Furthermore, in the latter scenario, that cash is eventually going to get deposited back into a regulated institution (to pay credit card bills, etc.). If anything, a person depositing thousands of dollars in cash on a regular basis is going to draw more scrutiny, especially if they're not running a cash business.
Which leads to the obvious solution: you're going to buy that Wendy's where you're exchanging your USBs for cash. Congratulations. You're now officially a money launderer!
While that's not to say that aged shells, nominee directors, etc. don't serve a purpose for certain people in certain situations, a lot of this stuff is just designed to enrich the service providers through fees and provides very little meaningful value in terms of privacy and protection.
A lot of Russians use offshore structures to protect their assets from the state. Also, Russia has a territorial tax system under which nonresidents are taxed only on their Russian-source income. Many wealthy Russians live overseas, so if you make your money abroad and live abroad, there's nothing inherently illegal about keeping your money abroad if you're a Russian.
Basically, the reasons a Russian would go offshore are a bit different from the reasons an average American would.
Finally, in cases where a Russian was offshore for shady business, you should recognize that the long arm of the Russian authorities isn't that long. The US, on the other hand, can functionally knee-cap financial institutions anywhere in the world for refusing to do what it wants.
As evidence of this, consider that even Chinese banks will comply with US sanctions if they feel there's a risk to their US dollar operations:
https://www.bloombergquint.com/global-economics/chinese-bank...
Big companies use complex international structures to dodge taxes and regulations legally. Currently, there are no reasons to do that for a random small business; if there is, there may be demand. Kinda like people register their companies in Delaware even though it doesn't make "logical" sense; just to (legally) get the regulatory advantages.
This is speculation, obviously, based on the direction this goes with the account surveillance.