I think Harry will be fine in California, he is not at the backwaters of the America.
The culture is familiar and he has been there lots of times. His cousins, have lived there. One of the York sisters lived in NY for years and they were seen partying together with Harry in LA plenty of times. Prince of Michael son has lived there for years and has children born there. None of them sound like they missed out on anything family related. H's BFF from school lives there, as well as the bff from army.
The US also has great schools, that people from the UK specifically leave for - randomly pick any private school in the UK and there is surprisingly high number of students who transfer to US universities. If one of the children wanted to take after their parents with work, MIC etc is not far away. There are also options for UK education should they wish. Whereas years ago, you either went home or they send you UK products that you like, nowadays all major cities have several international shops or you just Amazon for your UK products.
I can understand people who move to a very different culture like say Middle East, Asia, Africa etc. but this is not the case here..
People had been hoping for a while now that this couple splits, truth is, all those obstacles they place in front of them, may unintentionally have brought them closer together than they would have been.