The premise isn't it creates only good schools it's that it gets schools to be better on average.
I'd be interested in seeing some figures with regards to the number of home schooled children who go onto college and their success as a group in that setting. I imagine what you are noticing is actually more down to two things.
1 - Very gifted kids are a lot more likely to be home schooled as it creates a reason for it to happen so you have the random sample of people who are home schooled but skewed top heavy with gifted kids. Kids with very bad behavioural problems and those who struggle massively are much more likely to be in special schools or left in standard education.
2 - The thought of high school - college - university (and us equivalent) is a very standard path for kids in schools. It's where you end up if you don't really put all that much thought into it not to mention all the pressures on kids to take this path even if it isn't what they really want. With homeschooling there is much less likely to be that same pressure (as parents are kid of rejecting state education by homeschooling) so those that end up there are more likely to want to be there.
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