One of the many reasons is the often poor quality of state education. As I say, there are many reasons but once the parent has come to the end of the road (as often happens) they simply don't care about receiving "compensation".

That argument never holds water, as there are many services that taxes (apparently) pay for that many people do not use themselves and what about people who don't have any children - can they claim their portion of tax back for education they don't use?

I don't think it would make too much difference because the the reasons for doing so are often philosophical or they are forced into it because their child(ren) is not thriving. So they will do it no matter what and make it work somehow. If you feel strongly enough to do that, you are not going to care if you get a few bucks from the government and if you're doing it because you'll get some $$ then it's not for the right reasons. You're doing it because you feel compelled to do it. Sure there might be some who would do when they couldn't otherwise afford it but it's unrealistic IMO as they're never going to be paying people the full wage that they lost. It's usually just a few hundred bucks per year which, granted, some home educators (who are doing it on a shoestring) will take. Then there are ones who never take anything from the govt.

In terms of being "sovereign" I don't think home educators should accept money from the state. That opens doors that will ultimately lead to unwarranted control and surveillance. If we ask for money from the government we are telling them that it is their job to educate our children. It is not, it is our job. Why should we receive "compensation" for raising our own children? Here is a short article about accepting "free money".