The answer is generally the same as it would be for a parent who removes the child from the state system and puts them into a public school. Funding is available for children in the state system of schooling.
Whilst many home educators whose children have been deregistered from school, often start off thinking they would like to have funding from the LEA, many of us quickly realise that, if we received funding then the LEA/Government/public would expect to be able to judge whether they are getting value for money.
"He who pays the piper, calls the tune"
This would then mean that the home educator has to educate in a way that the LEA/Government/public would recognise and approve of. No way am I going to allow anyone to dictate how we educate our children, when every way that has been offered them through the state system has failed them so badly.
I would have liked free access to qualifications for my children when they were under 16 but I didn't want ANY money from anyone for anything. We want to be able to be able to educate our children in a way that is suitable to each of them individually. We follow a completely child led, 'autonomous' educational style, where there is very, very little formal work-and only then if the children have requested it. The children have never been seen by the LEA since the day they left school and they have never wanted to show any work to the LEA. We send in our 'educational philosophy' and a written report.
After five years of autonomous home education the older two are at FE college and have already done better in their AS levels than their schools ever suggested they could. They have settled in well socially and we have had excellent reports from their lecturers about how well they are doing.
I can't imagine the way we educated them would ever meet with approval from a LEA providing funds.
Many home educators are suffering severe hardship in order to free their children of the state system. It usually means at least the loss of one salary although there are some opportunities for part time work-I work from home for a DSA, selling clothes to ladies. TBH I would have gone to almost any lengths to free my children from the system which was failing them so badly.