An infantry battalion is equipped, organised and trained for all phases of land warfare, including limited and manoeuvre warfare and protracted offensive operations over long distances and away from firm bases, in conjunction with other arms (armour, artillery, air etc).
The RAF Regiment's main purpose, for which they are equipped, organised and trained, is to defend static installations (air bases etc) and their approaches. At that they are outstandingly effective. So they should be because their role is relatively limited.
There is no question that they should be part of any other service than the RAF, who operate the bases they exist to defend. It would be wasteful to task infantry battalions with the RAF Regiment's task. The current situation is ideal and needs no tinkering.