The more likely scenario is that the US govt declares Intel "too big to fail" and they give them a bunch of money. They are already doing that through the CHIPS Act.
But when what? OK, you've nationalized Intel. All the same people are working at Intel. You've bought Intel, but you haven't really changed anything. GovernmentIntel faces all the same problems that Intel faced like high US wages and having been behind on EUV lithography.
The biggest problem with Intel is that it ignored EUV for a decade hoping to save money. If the US nationalized Intel in 2012 and the government said "you're going to invest in EUV," then Intel would be in a different place today. Nationalizing Intel in 2024 wouldn't really do much. They've already changed course and should have High NA EUV chips out years before TSMC.
Of course, the US could have also just said "we'll offer billions if you invest in EUV fabs in the US" back in 2012.
I guess the question is: what does nationalizing Intel give you? It gives you control, but you also basically already have control if you're willing to give them money - and nationalizing companies typically costs more than incentives.
A government might keep things like shipyards in business, even if they can't compete in the global market, just in case we ever need a rush order of new warships. And keep steel mills in business to supply the shipyards, and so on.
Because modern weapon systems need modern integrated circuits, if there was the political desire the state could keep Intel on life support forever.