Paid for schools sell themselves to parents with their exam results more than anything else.
They may have a lot of equipment and resources that state schools don't have, but it's pretty irrelevant if they don't have grades to back it up. Paid for schools I'm familiar with will often measure their results by what percentage of pupils are successful Oxbridge candidates, particularly if they're studying classics.
The gimmicks such as laser cutters, 3d printers, green screens, recording studios, gym and sports facilities, personal laptops, art supplies etc etc. are pretty good for pupils who were never going to be accepted to a highest level university regardless of education. So you have selling points for higher and lower ability pupils.
Students take a contradictory side to their government.
And Bears do in fact shit in the woods.