@OhCrumbsWhereNow We're in the exact same boat. It's really, really hard to find a school for a child that's typical in everything but academics. There's so much out there for kids with ASD, even the Speech and Lang units in our borough are now all ASD units. Whilst I don't want to underestimate the struggles those parents have, I know it's not easy to get those places, there is literally nothing for kids with purely academic support needs. Even Fairley House gets quite ASD heavy in the upper years which makes it really difficult to meet the social needs of kids without ASD, given the year groups are about 25 kids.
There's a few schools popping up with Dyslexia ARPs attached to mainstream schools, like Orleans Park, but these are so rare and you can't guarantee quality. Plus, based on their SEN report, my DD actually gets more support in her state school without an ARP than what's on offer there. We've been through a few secondaries now, and I've worked in a few too. My experience is that the more SEN kids flow through your doors, the better the provision is likely to be. Which is why it's rare for those "leafy 4% FSM" type schools to have good SEN provision. They attract high achieving kids, the kids who need support often get it from home. Obviously not always the case but that's my experience. Even without specialist training, as a teacher when you have 30% with dyslexia or other SEN in every class, you will quickly learn the best scaffolding to use. You don't need to do ELKLAN or Level 5 SpLD training. Mainstream private schools just don't have that, those teachers are unlikely to get have that experience.
Also, on an emotional level, for a child to be in a school where there's lots of other kids with SEN, lots of others who are just like them and need support, it's very important. I think parents forget this aspect when they see the lovely tiny private school.
State schools also get a lot more access to cheaper LA training, access to their EP and SALT etc, and charities that are willing to work with them. Privates have to pay for everything. I'm not saying state is superior, but in my experience, for SEN profiles like my DDs, it has been.
Homeschool is great and DD did well over lockdown. My very close friend home eds and it is very popular with SEN families. It's brilliant but again, a lot of the older kids have an ASD profile, the socially typical kids tend to go back to mainstream around secondary, so socialising with socially typical kids can be difficult to arrange.