I don't like it! It puts me into that resistant frame of mind. The connotations are negative (you intervene between people, or to stop someone, don't you?). Why can't they use "assistance" "guidance" or "help"? At DS2's nursery the teacher says "input" which is better also - it reflects the significance of her professional role but keeps DS2 centre stage, as it were. "Intervention" ties in with the tendency of the professionals to talk about language delay late talking on their websites as if it was something that you diagnose and cure with antibiotics. Whereas in reality, having read all your testimonies, it seems to be the parent and nursery who provide the long-term support.
This may sound trival but as one of the thousands of parents who bridled at the thought of being "disloyal" by seeking help for my DS1, I think changing the word could be a good thing, bringing professionals and parents closer together. It didn't matter that I did nothing in respect of DS1 but it must matter for other parents.