Well, no, speaking as a teacher with quite a bit of experience in the state, private, & international circuits.
Quite often in private schools, you get parents who feel that because they are paying a huge wedge, they'd quite like that to be reflected in top grades despite the fact that their kid is one who'd be getting MASSIVE support in a state school for their academic struggles & (usually consequent) behavioural issues.
We don't choose 'the brightest'. We take kids whose parents can pay. & if someone's dc5 is academically weak, bullying their peers & liable to tell teachers to fuck off - we would generally not want to rock the applecart & upset the parents of dc1-4, who are doing nicely & generating a tub of revenue.
'Private schools simply won't allow it' 🤣.
I've taught in the private sector for quite some years, with my dc having free places. They've benefited - genuinely - from amazing facilities & opportunities.
But the actual teaching? They would have been much better served, I suspect, attending a good comprehensive, where the quality of teaching is monitored rather closely.
Obviously, you need good behaviour to teach well. That's down to effective systems, culture & SMT/HOD support. & it works, or doesn't, regardless of what is going on outside the gates.
Most kids would like to learn. Also, most kids will dick about if that's seen as acceptable, THEN grumble that they aren't learning. Because they're teenagers with poor impulse control & peer status/relationships are everything.
Give them a fairly robust approach to poor behaviour, consistently followed up, & most dc will be hugely relieved.