The facility of being to stay in a Mess away from your home Station was fairly useful when I was a young singly - I didn't use it
that often, but if I wanted to go away for a weekend (and if there was space available at a Mess near where I was going) it came in handy.
As for the Treasury worrying about servicemen obtaining a 'pecuniary advantage', I suppose that's typical of their attitude. If there was an empty room in a Mess, they didn't get any money for it and the 'fixed costs' of operating the Mess were still there. If I or somebody else used that room, then the 'Variable cost'- the cost of laundering the sheets - was more than covered by the accommodation charge.
Moving back to discounts/benefits available to servicemen: The Americans have an R&R facility a few miles from here (
the Edelweiss Lodge) which is certainly open to British Forces personnel.