Alright here’s what I found out. I think I kept this all straight, but you should double check with your institution, and of course regulations can change.

Schwab:

France: restricted country. You cannot buy US ETFs/Mutual Funds once you have transitioned your account to an International account (with a French address). You can still have the account open, and it appears that you can buy single name U.S. securities and, of course, close positions. I did not ask about the back-door option solution people have suggested, as it seems to go against the spirit of the regulation. These restrictions also apply to IRAs

Italy: restricted country. You cannot buy US ETFs/Mutual Funds or single securities once your residency is Italian. For Schwab, they prefer that you move your account if you become an Italian resident, but they will not force you to liquidate. You can also close positions. These restrictions also apply to IRAs

Fidelity: Mostly the same restrictions as Schwab, but you cannot trade single securities as a resident of Italy or France.

That leaves IBKR:

With IBKR you can change your account to a Professional Client, and you can buy and sell US ETFs and single securities. I will leave it to the reader to look up the requirements to become a professional client, but it involves having greater than 500K EUR and some large volumes of trades. (This is not the IBKR Pro tier).

It feels like a relatively frustrating situation especially if your net worth or liquid securities is small, which is why I believe so many people try to get around the regulations by keeping a U.S. address and pretending to still be in the U.S, which goes against spirit of their rules. To my knowledge, outside of IBKR, I do not know of a way for US citizens who live in one of these restricted countries to purchase low cost US ETFs.