I don't think we'd get 'betterment' of the Services if we decided to recruit solely from a limited sector of society. I think we have (on the whole) capable individuals from the broadest spectrum of backgrounds and experiences possible. This has to be better than selecting those who happened to have a certain heritage or their parents did well for themselves.
That ethos and spirit is in those people who arrive through the gates of Cranwell. It is up to us and our lords & masters to perpetuate that spirit. I know I get precious little of it from above but do my damndest for my charges to get them on training, sport etc. We must get it right within our own walls before we look outside for an answer/solution. The steady erosion of what I joined for (AT, sport, more of a life than a job etc) are doing the damage - not who we let in. Enthusiasm is whittled away more than it is encouraged.
Yes - I KNOW anyone can pay to go to a better school - but that creates another sort of class system - cash. A scrap merchant may have as much ability as Lord Wally de Honk to send his little ones to a 'good' school, but it still excludes others who are capable. Also, paying for education does not make it better - just paid for.
I am not some class warrior here, but the tests are set at IOT and anyone can sit them. Regardless of which school, it is about ability.