I wasn't happy at private school because it just wasn't a good fit for me
The children still were capable of bullying (I wasn't bullied but a close friend was bullied badly by some mean girls). The teachers at my state school were much nicer (and better teachers by and large too).
I had plenty of opportunity for nice food at home and thrived once I was at a state school (topped up by tutors, music lessons, sailing lessons and horse riding). Got into Cambridge and got a highly sought after career.
My brother went to private school and was probably happier there but he switched to state for sixth form (just because they had the subject combo he wanted) and was shocked that there wasn't the pervasive drugs problem that there had been at his private school.
My youngest brother refused to go to private because he didn't like the longer journey. he had a huge group of friends, got on really well with his teachers and never once questioned his choice. He's the most successful of the three of us. Both nationally successful in his chosen sport and professionally phenomenally successful.
It's just not a binary. I would send my children to private if I felt they weren't thriving but a the moment they are really happy at school, and we have heaps of spare money for hobbies, holidays and saving for house deposits for them.
I agree its a privilege to have the full range of choices, but the right choice won't always be private. Round here private schools are either very much non-academic (and my children are very bright) or are in the centre of cities with an unpleasant journey by train or road to get there