We've chosen hyper-specialization of our living areas. The places which are good for raising children are mostly horrible for careers and social life. The places where young people can get ahead and be social aren't as traditionally convenient for raising children (unless you have lots of money).
You pretty much have to pick where you live based on what phase of your life you're in, and I think for most people the expectation is still that once you get married you'll just move out to the 'burbs. Personally, I hate the idea, but I'm both not in a place in life where I'm too worried about children and also fortunate to work in an industry where its at least theoretically viable to afford to raise city kids and maintain a career.
My parents are getting ready to retire and thinking of moving to the mountains somewhere because being retired is no fun in a place where everything is optimized around children and everything is developed family-size. They won't be a support system where they are for my hypothetical kids anyways, and are eager to escape the suburb I grew up in as it has declined over the decades, so I wouldn't want to be there either.
Wrapping up that rant... quite simply, I insisted on moving away from where I grew up because there was nothing for me there and I wouldn't want my kids to grow up in that place. The fact that my parents still live there for now is mostly incidental. (But I also generally think suburbs are a worst-of-both-worlds kind of thing, none of the cohesive culture or community of a small town but also none of the variety, walk/bikeability, or cultural diversity of big cities, so my bias might be showing).
So we moved out to the burbs, where we could afford a starter home big enough for our two kids and a mother-in-law.
I guess it's already happening to some extent with Schengen and young talented engineers moving to job centers.
Because over a several hundred year period a large fraction of the people in Europe who were willing to risk financial ruin for a chance at a better life wound up here and our culture reflects that.
What you experience is still quite common. Some of my siblings live 5 minutes from my parents and my nieces & nephews basically stay with their grandparents while their parents are working. A lot of my coworkers claim similar situations as well.
That being said, multigenerational households were really common up until the postwar period, at which point the US really started pushing the standalone suburban nuclear family as a way to avoid another case of excess industrial capacity. It takes a lot of workers and goods to build all the highways, infrastructure, and houses to support a two-story house with a white picket fence and a car in the driveway.
Go west young man was not just a saying but part of America. Look at post WWII information on families moving to California for example.
But this means that when your children decide to have children, they will have to move away. If they are lucky, they can buy a house near you; but if there are many people who want to live in the city, and the new houses are not built often, or at least not near you, then they will have to move further away from you. And this is still just talking about living in a city... I haven't mentioned proximity to job opportunities or schools yet.
If you don't live in the larger metro areas, there aren't the same number of jobs paying good wages. So you move to where the jobs are, or at least where the jobs you want are. If you're a software developer you probably don't want to live in Ohio, and if you're a defense contractor you probably don't want to live in Wyoming.