It all depends on the needs of the child. At secondary a child with an EHCP who is high achieving in maths/physics but with significant ASD/ADHD needs will be funnelled to lower sets where the TAs are available. A highly academically able child with social needs is difficult to place as top sets don't have TAs and the school will argue that an LSA is detrimental. So best place them in the lowest set.
I absolutely support private placement in non specialist schools for DC with an EHCP whose needs cannot be met in mainstream because they are unusual in presentation. It is a travesty that parents of so called twice exceptional DC have to go to tribunal or pay for additional support even if placement is granted.
But this is not the norm. Most SEN DC in private don't have an EHCP and this is because they don't meet the criteria not because parents choose not to increase state burden. It's precisely because their DC don't meet criteria for support that they do the sums and opt for private. Most parents can't afford private when state is not good enough. There will be some parents who opted for private who could barely afford it for whom VAT will be a deal breaker. There will be some parents without SEN DC who are politically opposed to VAT. There are choices.
If private schools want to support SEN DC they could waive the VAT or provide bursaries, especially if they relied on back up from this cohort to survive. But they seem to be doing the exact opposite with even Eton cutting bursaries.
Why would they do otherwise. They are a private business not a pubic service.
But don't believe the hype that if you remove your DC there will be a huge burden on the state sector because DC that don't need an EHCP in mainstream private will need one in mainstream state. I'd be surprised if their needs were not judged able to be met from normal SEN budget.
But at least you will have thousands to pay for tutors/private reports/solicitors/tribunal instead of school fees.