It's funny how people will gut the foundation of public education over decades, then turn around and point saying "Look, it's shaky." Of course it's shaky. It's chronically underfunded, teachers have no say over student behaviour and no control over the curriculum.
Why? Public schools are funded by tax money, not by the kids. Less kids using public schools mean more resources for the kids left. No?
I am not following your reasoning.
Can look at some links about this:
https://www.nheri.org/home-school-researcher-the-impact-of-h...
https://responsiblehomeschooling.org/the-homeschool-math-gap...
The data from Alaska is based on "students are enrolled in the state’s popular correspondence programs". If that implies state control of materials and syllabus it is more like school than real home education.
I think you are right in so far as there is a particular sizeable group (affluent hippie women in my experience in the UK) of home educators tend to encourage humanities and creative arts.
It looks from these UK numbers (also admittedly not recent) that HE kids do better at maths here: https://core.ac.uk/download/108200.pdf (page 298).
In general, the internet has been of huge help to home educators: online classes, better access to resources, online advice and community (only useful thing I have ever found on Facebook are HE groups!) so I would expect that to have had a major impact.
We also survived covid lockdowns rather better.
Your statistics support the previous claim. If you have a group out performing the public school by 15 to 30% there will be more spread in educational outcomes. Many would see that as a good thing when some kids get closer to reaching their potential, but not everyone wants that.
A 2016 study by the National Home Education Research Institute (NHERI) indicates homeschoolers scored between 15 and 30 percentage points higher on standardized academic achievement tests and usually scored higher on the SAT/ACT.
https://www.nheri.org/research-facts-on-homeschooling/