I periodically visit the United States on Travel visa. Usually for up to 6 months. I have been self-employed in the EU (EU national) and I know when I visit the states I'm not allowed to work for my US clients. I don't do this in order to be sure that I can return to the US when I would like to in the future. But this also prevents me from working, now think carrier wise not income wise. I would like to keep working while in the US which is not allowed. Would it be any different if I would use a limited company (my own, somewhere in EU) to bill my clients? As such the revenue will go to the company not me and all the contracts will show the company not me. From purely legal perspective. I know that with the remote contracting, there is actually a very small chance that the USCIS will even know about this but that's not the point.
Common sense would suggest that it doesn't matter as long as I work for US clients and the company is actually mine. It would be maybe different when the company would be a German agency or such.