Penstemmon, I agree absolutely that children in mainstream school shouldn't usually need 1:1 help, apart from specifically targeted lessons. I expect you know that the Labour government funded schools for Maths and Literacy 1:1 support, but this had to be given by qualified teachers NOT LSAs. That funding has now disappeared into the general budget and is no longer ring-fenced.
Your description of the ideal scenario is wonderful, but in my experience not realistic. As a secondary teacher, most of my classes had over 30 pupils and it just wasn't possible to give every child in the class individual attention. If a SEND pupil also happened to have behaviour problems, this severely affected the learning of all pupils.
When I started teaching in 1982, a percentage of SEND pupils were in special schools, but gradually they were closed, probably with the best of intentions. However, nobody really gave any thought to how these pupils would cope in mainstream schools. Funding and training were (and are) inadequate. In thirty years of teaching, I never had any specific special needs training. Teachers were just left to cope as best as they could. Boxes were ticked by employing TAs and LSAs, but in my opinion the pupils with the greatest needs shouldn't be fobbed off with the least qualified staff. TAs in secondary schools aren't the best solution. I also have to say that if I had had a child with certain special needs, I wouldn't have wanted him/her in a mainstream school.
Crafting, as a matter of interest, what kind of help is being given in the new school?