Home ed parents will pay as much as other taxpayers and then more so.
And parents with school-educated children pay as much as other tax payers, and then more so too. I do both - and one child who is part-time of both - and all ways of educating have their additional expenses alongside benefits, risks, and responsibility. I've spent more, on a tighter deadline, for my kids to use schools than to educate them at home.
Local authorities may need some incentive to ensure more children who should be in school are, which might include them having to give financial support for families in that situation, but I can't see what benefit incentivizing home education is at this time.
As a teacher myself it baffles me how unskilled parents think they can give as good a quality education to their children that's taken me over two decades to acquire the skills needed.
As many other posters said, home education in the UK is widely done by those who've tried the school system and been failed. For many, the choice isn't a quality school vs home education, but a failing school or a school that has failed to provide for SEN needs or prevent violence or a lack of a suitable school place and home education.
How quality education is defined varies widely both on a population level and an individual level, but even for those of us who choose to home educate it's within our options available. For primary, I try to do something different than can be accomplished in primary schools with all they are required to do to measure outcomes, with far too little resources, in an area with failing schools.
I'm not trying to compete with teachers, I'm dealing with the systems around me the ways I can. Sometimes that's home educating, sometimes that's working in a school academy trust (even as an unskilled parent).
If I had different options, maybe I'd have chosen differently - much like my children where the ones who had the option of trying the new non-catchment secondary chose to take the potential risk with the possible benefits, while my eldest whose only options were secondaries more known for people getting glassed than outcomes chose to continue learning at home until he could attend college.
Because presumably they care about outcomes for home educated children.
I think the government cares about as much as the outcomes of state school educated children - which is questionably, but definitely not enough.
That's actually a big part of why I don't want them to focus on incentivizing home education. Exams, better access to service and inclusion, sure, but the education systems have enough cracks to focus on that I'd rather schools that off-rolled or refused to put in appropriate measures to protect and better outcomes for all children weren't given something else they could push at parents to make their children not the school's problem rather than the school actually fulfilling their responsibilities. Sure, some dodgy parents might take advantage, but I can see some dodgy schools doing it just as much.