There's lots of DC on the SEN register who don't have diagnosed SN or are not impacted to a degree that they would qualify for an EHCP (assuming appeal).
Private education is still a choice that can only be made if it is affordable. Because you are not paying fees for SALT or OT or specialist dyslexia teachers that you can't get in state but for small classes, extra-curricular etc which also benefit non SEN pupils. Most private schools charge extra for specific provision.
So all you are saying is that private benefits non SEN and SEN because of environment. OK. But if you think so you have to buy it and if VAT is added, that's the cost.
There are some small private schools that accept DC with an EHCP but most run a mile. Maybe that's part of the reason that parents claim that a lot of DC without EHCPs are in private.
I am still confused by documented crisis in state and the how threshold of needs not being met is arrived at. Is this just something parents say or is it based on LA criteria - it is part of the process for EHCP and appeal for independent. If private is not an option you apply for an EHCP and fight. If private is an option, it's a choice.
Sadly, I think that some posters are forgetting that some DC are hugely disadvantaged by their diagnosed SN that impact on their ability to ever live an independent life, even if they attended indi, and are using them to decry a fair tax that has nothing to do with SN.