9/11 (hear me out on this...)
I have a theory as to why the dad took the decision to basically lock up his children (until they rebelled or whatever and finally struck out to find their own jobs and places and so on, and this is aside from the fact that he has some mental disorder): 9/11. There's a very brief shot, taken from the family home-video footage, where the dad is describing coming to New York city as a stop on the way to Scandinavia or what have you, and it's a shot of the Twin Towers. Clearly if they were living in NYC at the time then this was right in the area where they were in the midst of all of this terror and horrors of the attacks. I think that this caused the father to snap and decide that the city would not be safe to take his kids out into (logically it wouldn't make sense to keep them "locked up" in any case, but in the 21st century crime has gone down in the city compared to the 70s-80-s-90s).
It's just a theory, and I'm going by a very thin piece of evidence, but it could explain a lot.
iTunes podcast: https://itunes.apple.com/us/podcast/the-wages-of-cinema/id977881387?mt=2/