I think you are underestimating how tight for space some schools are.
There simply isn't always spare classrooms, a suitable office space, etc. If the room isn't there what can they do? they can't just make room where there is none.
Many primary school libraries are open plan, off a corridor - so not suitable for most of these kind of interventions.
Many schools only have one office - the headteacher's, which all of SLT need to use and will have confidential paperwork on the desk/walls so not suitable for an external agencies.
The hall may be big area, with a walk way through, and needed to be used by a tight rota of classes doing pe, singing, drama, lessons etc.
And it won't be just one child/one agency. Most schools these days have several children with needs. We have a series of interventions, affecting many children, right across school. These have to be fit in and space found.
If only it was as simple as just finding the space.