"Many of the home-schooled children I've known have been odd, too, but I think that's why they ended up being home-schooled - they were odd and struggled in school"
This ^^. I don't see how the Swedish model would work for these children, or do they receive a lot more support than their counterparts in the UK?
"but I was totally burnt out.mental health down the toilet..so they had to go to school..I didn't give any time or attention to myself or my husband."
This is one of the reasons I never wanted to home educate. With younger children there is no child free time unless you have a good support network (which we didn't have)
"Look at the schools cutting GCSEs like music and arts because they don't fit in the narrow band of the English baccalaureate"
I doubt very much if that is the main reason. It is to do with the serious problem of underfunding in education.
"As a H/E your science lesson could take place on the beach, your geography lesson could be made up of planning the journey to the beach, the maths lesson is working out costs of travel to beach, buying an ice cream, your English lesson is reading three pages on the beach."
Which is fine for primary age and excellent life skills, but not enough for GCSEs and A levels.
I kind of get the impression that most of the home educators I have read about on here and elsewhere tend to be teaching children of primary age. When it comes to KS4 and KS5 outside agencies become more involved because of the level of learning or resources required, but I am happy to be corrected.
Home educating wasn't for me, but I wish all the luck to those who do.