The problem is f-35 brings more American oversight than being in an actual treaty alliance with America.
Most countries, especially in Europe, honestly don't care about this. It's more like the benefits of a much closer relationship with the US outweigh the cons. Also, their "oversight" isn't really a big problem even for countries like India, let alone Europe. Like the Americans want to protect their communication and encryption systems. Such things don't bother even India.