The services would still need dedicated hospitals because their injuries will always require specialised treatment.
Not that long ago all three services had a number of hospitals exclusively to treat their own personnel and service families. In emergencies they could be and were called upon to help out the NHS. They were funded entirely by the services out of their own defence budgets and were staffed by service nurses and doctors. They were excellent but once again the government saw easy money in shutting them down and selling off the sites.
All part of the great betrayal of the armed forces. If you want people to be prepared to fight for you then you have to look after them ~ FFS Alfred the Great recognised that but Blair and Brown did not.