Ameribro here. In the ideal world it seems like a reasonable approach: send your kids to get UG degree in your home country (save tuition money, may be even get better education etc) and then they can apply to a PhD in the US, if they want to. It's hard to get to US job market with European PhD. But to get into US PhD with a European degree so no harm done.
But the reality is, if your kid grew up in the US they are American. And they can be fluent in, say, German. But they will still be lacking all the references, cultural fluency, experience of going through German high schools etc. Imho they will be outcasts unless they are some uber-social Chads. Given that, not sure they'll want to do or it's worth do it. This is imho, of course, since I don't have to deal with this issue myself.