The profile of need you mention (non-verbal, violent, severe behavioural issues) have specialist provision, state and private, made for them. Able, anxious autistic kids who are scared of anger and can't cope with too much sensory input don't. Schools for them don't exist in the state sector, and the private sector is really poor quality, on the whole, at disgustingly high cost.
My child is in a class of 15, and she is the 4th autistic child in that class. It's a small private school, and not hideously expensive by those standards but still, agreed, way beyond normal families. But two of the kids are from those normal families and they are working extra jobs and remortgaging to afford it. Mine, and another child, are on EHCPs. There are also two schools in a neighbouring town that are more than 50% EHCP kids, because the LA are using them to save the cost of even state specialist. It probably varies area to area but in ours, at least, some private schools have higher SEN and even EHCP levels than many state schools do. There's a private school in the next county that has a third of their kids on EHCPs and an autism base. I genuinely don't think people realise what has happened in SEN provision these past ten years, or how councils are trying to find alternatives to specialist, given state specialist costs more than mainstream private and private specialist can easily top £100,000 a year when travel is factored in (and some before it's factored in, too).
It's also worth remembering that quite a lot of kids who match the profile you cite match that profile precisely because they didn't get needs met in time. They didn't, mostly, start in primary aggressive and angry. Mainstream destroyed them. I know too many families like that, whose sweet, oddball KS1 kids are now enraged teenagers in SEMH settings.
The issue is quite discrete, though, and I don't think it would actually impact the whole VAT argument, if a carefully considered, sensible exemption was created. At the moment, you need an EHCP, and since Covid getting through the system takes a year at least and often two. It's perfectly possible for people to support the VAT being levied, and also feel that exemptions for SEN should be more widely and carefully targeted.
Basically, if a parent can prove that a smaller, gentler setting is a need and not a luxury good, then they shouldn't pay the luxury good tax. We don't on sensory aids if we can prove it's for a medical need and not a fun toy, as an example. Same principle on a larger scale.
And again, mine has an EHCP, so I am not personally affected. I just feel the exemptions, where it isn't a choice, should be there.