In my experience you shouldn't need to do this. In fact, I suspect doing this creates both a taxation and legal nightmare.
You should have a registered company (or any other trading entity) so you can bill as an independent contractor. However, it should be registered in your country of residence. Services like Deel exist specifically to facilitate this sort of arrangement, it's a breeze.
If you register a company in the US, you can't just arbitrarily transfer the money to yourself internationally. You'd need to pay yourself as an international independent contractor anyway. Except then you create legal issues, since there are likely legal issues with a company you run hiring another company you run. Additionally, by operating two companies, you're presumably filing two company tax returns, and paying yearly registration fees for two companies.