A lot of people forget that the those troops are the very reason Japan, South Korea and many other countries in the region haven't developed nuclear arsenals themselves. The post WWII agreement has essentially been "the US promises to protect its allies and in exchange they limit their military investments and don't pursue nuclear weapons".
As much as China might not like US bases in neighboring countries, it's a lot better than if all of its neighbors had or were in the process of developing nukes. That scenario is a nightmare with too many ways of going horribly wrong.