Actually no I don't think most people support home schooling
But I also think there's a lot of wrong on both sides of the table about this.
The socialisation is a crap argument. I sent DS to school because I worried about this. He never made a friend there either. He was just bullied. If you are slightly odd there's a good chance you will be slightly odd either at school or home, just you'll be happier in your own space. You can't educate out oddness, School cannot and does not actually teach socialisation.
Many children are happy learning at home. Covid has told us this is a fact. We should support this.
Too many home schooled children don't do enough formalised learning. Or at least that's what many people not home schooling believe. I'm not sure their wrong actually. As far as im concerned The state should still be insisting that home schooling children take at least GCSE maths English and science and funding it. It is challenging to find places prepared to take external candidates and costly, I can see why some people don't bother.
We are seeing much success with online education systems. I have absolutely no idea why govenment don't fund an online school for those who would benefit from it. I suspect you would suddenly see a considerable reduction in those "home schooling" independently if you did this.
Asides from SN a large number of children are home educated for religious or philosophical reasons. I worry these is actually very problematic and limiting for the child who might otherwise reject unhealthy values when exposed in a more open schooling environment. Whilst home schooling is not and should not be a safeguarding risk, too many children who are at risk get lost under the guise of being home schooled. The homeschooling community is and has been too slow to recognise this. A register was always inevitable. Sadly where the community has fought any kind of oversight, (to my mind it is absolutely correct that physical evidence of learning should be provided to the LEA and a yearly home visit done) it is likely that a overly draconian regime and testing system will result. They was time for a negotiated solution but it was lost by a very militant branch of the Home schooling population sticking their hands in their ears about real would safeguarding risk.
Homeschooling can be an incredible thing, but it needs proper support and oversight