Hi KSM - we have lived and travelled to very interesting and often challenging destinations with our children over the past 10 years. Not the way you put your hypothetical question, but close enough. Yes it is hideously expensive to live in the global corridors.
We did, however, put the kids into a mainstream PYP/MYP/IB school which is IMHO the best system for global world walkers since it is about fostering internationally mindedness rather than viewing the world through a Euro or Ethnocentric lens.
Yes, they did learn a lot from all the cultures we lived in, developed a 3 dimensional whole world view which is not possible from normal travelling, reading, movies, TV etc. That said, I would not rely on just on exposure to cultures for education. Kids still need an academic framework against which they can relate and apply their experiences and knowledge in a critical way.
We are unfortunately now living in a country where the local schools and education systems are atrocious and no international options are available (not in our city anyway), so we will be doing internet schooling until we move to another destination again.
It is all about balance - school, family, society.
My DS (now 18.5) had his first day at "school" at 18, when he went into college to do A-levels. Both my DC were HE from the beginning and now have two heads are perfectly normal young adults. We didn't travel the world much (and we are not rich) but we did pursue interests in greater depth than we would have been able to if the DC had been in school.
Why do you think people have to be rich to home educate?
I was wondering the other day what my Kaden would turn out like if he didn't go to school and was instead educated by travelling the world and seeing other cultures. I know I have seen some telly programmes about it and i definitely not rich enough to do it lol, but have anyone on here ever known anyone who has educated a child outside of the system?