The MOD schedules are such that you have to operate three flights in each 14 day period, with the days changing slightly as the programme rolls forward. It makes it impossible to schedule any other regular activity with the aircraft alongside the Falklands operations.
You therefore end up scheduling three long-haul trips for the aircraft in 14 days, which is hardly high utilisation. As a result, to make it work, you need an aircraft which has relatively low lease/ownership costs. I can't think of one UK long-haul operator which is so equipped at present - gone are the TriStars, 747s etc and everyone now operates aircraft like A330s or 767s which are expensive to lease.
No UK operator with its current fleet could therefore make the contract work given the schedules which the UK MoD requires. The contract has therefore gone to a non-UK operator in the form of Omni, operating its DC10-30s with low capital costs.
Unless or until the MOD schedule changes to enable the aircraft to be used on other things, no operator with third-generation aircraft will be able to compete for the contract. It is therefore tied in to using older aircraft, which Omni have. That said, an old aircraft is not automatically an under-maintained one as some may argue.