> Where someone lives is the biggest investment they can make. It cannot be collected by rich people, and even poor people invest where they spend their time

All of these arguments apply to citizenship too, even more strongly. I've lived the majority of a year on three different continents, but have never changed my citizenship. It's also not accurate to say that the rich are less able to take advantage of this: the fact that I was able to try these things out is precisely because I'm rich.

I don't think the newcomer/old-timer distinction mentioned upthread is especially useful, for the reasons you already outlined. But formal citizenship maps almost precisely to being invested in a place: it's a commitment that you identify with this society and its future, (mostly) to the exclusion of any other society.