However, it is the public school system spending (on average - it varies even within states) $10,000 per child, and it is the PARENTS spending whatever they choose to spend on their child's curriculum. Some parents spend much more than $500, some spend far less. I spent $500 alone on just dd's foreign language (we use Rosetta Stone) and $250 on her chemistry, because it came with all the chemicals and reagents we need for the labs. Her math was about $100, English was $250. I was able to buy the history book used and spent only $10. We won't talk about what I spend for dance, band, music lessons, and riding lessons, as although that "counts" as music and PE for her, public schooled children also participate in (and spend money for) those type things. But we definitely do not need the public schools spending ANY money on our children, and at this point they do not.
I'm not interested in any help from the government. On the one hand, extra money would be nice, but on the other hand it would concern me that it could entice someone to homeschool who is otherwise not motivated to educate their children. It's not something to venture into lightly.
Also, usually government money comes with strings, and I would rather DIE than give someone the right to pop into my home uninvited and unscheduled. No, I have nothing to hide, but the 4th amendment gives me (and all law-abiding citizens) protection from unreasonable searches, the right to be secure in my own home, the right to privacy. If there is reasonable cause, then yes, the government has the right and even the obligation to protect my children from abuse and neglect, but if I am doing nothing wrong then please leave me alone, thanks.

I don't want some stranger coming in and deciding that I should or shouldn't teach my DD the way I do, any more than they can decide where -or if- we attend church, or what I serve for dinner.
As for the argument that only parents should fund schools, as long as we have the public school system in its current incarnation, in other words, it is still the main - and for many children the ONLY - avenue by which our citizens are educated, then it is a public service that should be funded by all, just as we pay to pave the roads or staff the police and fire departments.
Should only those whose homes catch fire pay the salaries of the firefighters? Of course not. In the same way, we all benefit from public education. If we don't pay for schools, and parents won't/can't educate their own children, where will the future workers come from? Where did most of today's workers come from? Now, in my own little dream world, everyone would home school, so there would be no need for our tax dollars to be spent on public schools.

However, in Real Life, I know that homeschooling is not the right situation for every child or every parent, just as public school is not right for every child.
I read a great article several years ago that actually gave an objective list of the pros and cons of public, private, and home schooling, comparing and contrasting the good and the bad. Which one is best for a child should be decided by the parents. We've actually done all three - lol. My older DD went to private school for 3 years, then public school for 3 years, and we're starting our 3rd year of homeschooling. My younger dd did private school for 1 year, and public school for 5 years. She will come home next year. It's all about what's best for the individual child and family.