The only valuable US territory for EU nations to host troops would be Alaska and the Pacific territories, and Alaska would be the only decent location for European defense. Any other locations would only be useful for power projection, in which the EU seems rather disinterested in.
That said, the US hosts a lot of training centers for EU troops, including hosting a ton of pilot training schools. So there are a lot of EU troops in the US, they are just on American bases.
The only valuable US territory for EU nations to host troops would be Alaska and the Pacific territories, and Alaska would be the only decent location for European defense. Any other locations would only be useful for power projection, in which the EU seems rather disinterested in.
That said, the US hosts a lot of training centers for EU troops, including hosting a ton of pilot training schools. So there are a lot of EU troops in the US, they are just on American bases.
Maybe the French? That said, the EU is not directly benefiting from the petrodollar, so there’s no point in playing world police American style.