Have - each year I have an income. It is taxed. I have money left over to spend on anything I want. Inevitably this includes bills and housing costs etc. If there is anything left over then, I can spend it on anything I want - holidays, new car, private schools fees. The fees come out of post taxed income. That is why private school parents think they are paying "twice" for education.
The private school is a registered charity (because it provides education and falls into the definition of a charity). As a result they can claim charitable status and not pay VAT (I think). Should this be removed, or the school decide it no longer wants to be a charity, parents would pay an additional 20% or so on the fees. However, the school would then not be obliged to share its facilities or teachers, work with local state schools, give bursaries etc, as it is at the moment in order to maintain its charitable status.
I don't know what you mean by "you reduce the amount of tax you pay by using the charitable status offest"....I pay my tax before I decide if I have enough spare cash to pay for school fees - a discretionary item.
Enormous was saying she saves the state money by not taking a state school place (at the cost of £5.5k per year). She is still taxed on her income (which contributes to the education bill for the country), does not use the service, and pays for her children to attend private school (which employs teachers paid by the parents who send their kids to the private school). If you send your child to a state school, you are costing the state £5.5k per year, but of course you've paid for some/all of this through your tax bill, deducted from your pay each month.
If parents choose to donate to the school bursary fund then they are allowed to gift aid it, as it is deemed a charitable donation. This payment is discretionary, not compulsory (unlike the fees), the same as any charitable donation, and many bursary pots are monies raised on top of the school fees from parents. Only schools like Eton have a historical endowment for bursaries and plush buildings which they manage very efficiently through investments etc.
Parents at the private schools I know manage their old boys/girls network efficiently and encourage them to contribute to fund raising, as well as come and give talks to pupils etc. Robert Peston set up a brilliant scheme called Speakers for Schools for the state sector. I don't know how widely it is used, but I found the website very interesting.