As the schools nearby were full, I suspect the LA is obliged to pay for transport because it is, in effect, the nearest school with vacancies. The LA is obliged to offer a place and the parents have a right to accept it. As a result, the dc is awarded transport to school. Which has now been awarded. The parent did not really choose it and why on earth should anyone home educate? I could not have done it plus it would have been utterly wrong for my dc.
In this case, I would also suggest the parents don’t have high paying jobs so probably struggled with fees but dc didn’t get a bursary either.
The big issue with this vat hike is that LAs have not been able to plan for additional places that might be needed. Lincolnshire is rural and if a school is full that’s closer, then it’s highly likely another one is 25 miles away. This school was forced on the parents and they won’t be the only parents in this situation. Not for 1 second will Labour care about costs this policy brings about because the vat hike is about punishing the better off.