You make a point, I do not know how it would sit with the upper ranks though, but that sounds good. A US Foreign Legion would need to have very strict training methods that are a bit on the old school back then, english only language just like FFL where French is the language you must learn one way or another even by force, 5 year contracts, and also depending on performance, or if they are wounded in battle, US citizenship if they deserve it but they have to master the english language and pass an citizenship exam.
Also one other reason why a USFL would be a great thing is the FFL in my opinion is an example of diversity and assimilation done right for regardless if you come from Africa, Eastern Europe, China or Japan you learn French, and the culture and leave yours mostly behind to fit in and legion members who come from this could become better citizens in my opinion.
I would go further with a USFL. That is, while its officers are US military, it should have civilian leadership there as well, for several important reasons.
1) Democrats would always hate them, and a Democrat POTUS and congress would seek to destroy, disperse or abandon them, like they did to the ARVN.
2) They should perform individual missions on contract, with the right to refuse contracts they feel are grossly unfair or high risk. When they do carry out a contract, the *organization* is paid up front, not direct to individual members. And the organization controls the money it has been paid, not the US Treasury.
3) No citizenship agreement at all. Unless they are Americans, this is strictly contract work. They have to operate under bilateral treaties the US has created with other countries, so they will not be under threat from the International Criminal Court (ICC), that would also hate and want to persecute and destroy them. Oddly enough, *not* having US citizenship would bestow a lot of advantages on them.
4) Their civilian leaders, not the Pentagon, and not the US government, would create their Rules of Engagement, mission parameters, and duration of mission. No bureaucrat would be able to impose rules or restrictions on anything they did.