This would be a nuclear option and, in reality, probably would do more harm than good to SpaceX,
It would probably set back their more ambitious targets by decades. But even Starship is now far enough along to no longer really need Musk's stewardship, and the US government would be happy enough just with control of the Falcon programme. They don't care much / at all about Making Life Multi-Planetary.
I don't, Musk is too influential. And honestly, I don't think there needs to be much concern about space launch part of the business. I'm under the impression that it is already regulated enough to be relatively safely under control. And I would be sad to see it taken away from SpaceX and probably even Musk specifically. He is an incredible idiot and dangerous person, but the progress they did and triggered in others is undeniable and I'd like to see it continue.
But Starlink is a completely different matter. Private company strongly lead by a single, somewhat crazy person, is very dangerous. I think few people expected it to be such a game changer in the beginning, I certainly didn't. But it is important and very influential. Maybe ideal would be if it was controlled by the government, if it had the final say in geopolitical decisions etc., but the profits (or some part), development and such remained in the hands of SpaceX. Well, some international body as isolated from political influence as possible would be even better, but there's no chance of that happening.