Lots of pensioners don't "need" the state pension! It doesn't mean they're not entitled to it.
In this case, assuming the child is "entitled" to a taxi under the rules, then why the hell not should it not be provided, the exact same way it's provided to everyone else who is entitled by virtue of the distance they are forced to travel to the only available school.
Why is it different because she was previously privately educated?
She won't be the only child who gets a free taxi even though their parents "could" afford to pay for it. It's NOT means tested, and that has to apply for everyone, not just the ones who Labour voters hate!
The answer is to means-test the taxi provision for everyone, not just those who Labour voters don't like!