Well firstly, most DaDa schools are not providing degrees, they are usually diplomas (plus A Levels at some schools). Secondly, DaDas only pay for tuition, not boarding/living/accommodation costs which parents have to fund themselves. This makes DaDas impossible for lots of parents. Parental contributions towards fees are on a sliding scale too, so they are means tested.
Personally, had my child the talent, physique, work ethic etc to get a place at a DaDa school, I would not say to her "sorry, you can't accept your place because the Government should be funding more nursing posts". Most children successfully getting into DaDa schools have sacrificed so much of their childhood/social life to ballet or drama.
Knowing the Tories, if they stop DaDas, they are almost certainly not going to put that money into training nurses. 