I also really like this movie!
One of my first thoughts, when I heard about it was: Does this movie portray homeschooling in a way that makes it easier or harder for me to explain it or defend it if necessary? After watching it I think it does more harm than good to homeschooling. Like most movies, it brings everything, including homeschooling in this case, further than what is realistic. Capitan Fantastic certainly educates his children, but they are at the same time completely ignorant of current human culture, and could not function in the world as it is today. That makes it an interesting movie but not a good example of homeschooling.
I like that the movie shows this struggle and that their extreme level of education still lacks many important life skills. I also like that it ends with a compromise where they don't give up all of their former life but no longer hides from the world.
Do I like that they end up going to regular school? No, not really, but I think that it is the easiest way to show them coming out of hiding and start learning how to function in "normal" life.
I think you're right. It's a way extreme example to be sure. However, I feel like it is taking a little more of a shot at preppers specifically, as opposed to all homeschoolers. Like I said, though, I do hate that whole premise of us having to prove it's a valid option by showing our kids are smarter. For me that's totally beside the point. Freedom and separation from toxic mainstream culture and learning to be responsible and guide your own way are the main points for me. It would be nice, though, if there was a portrayal of homeschooling as it really is with kids interacting with lots of people of all ages all the time.