But as @OKBobble says it is a choice. I knew when I sent my dc to the school they go to, which has for years been consistently the best in the borough, I would be shelling out for numerous things each year for them to participate in as mentioned above (and I won’t lie I do eye roll every time another email comes through requesting money for ‘something’).
Like wise we almost sent ds to an indie, but he choose not to go. Had we sent him, it would have been our decision to pay those fees. Also many indies charge for exams on top of their fees, as the one ds looked at did.
You made a decision to home school your dc. Therefore you knew that there would be costs involved. You had the opportunity to send them to a state school and not pay the monthly fees you say you do, pay for exams to be entered, pay for outings, electricity, heating etc. But that was your choice, no one made you.
So if you decided to decline the offer of what is ‘free’ education, declined to pay the fees for an independent school, then why should the government pay for your child to sit exams?