I think you'll find also that SID's use flight levels and altitudes for the initial climbing levels. If there was a high transition altitude then in the initial climb from take off through the TA would involve three changes of pressure settings, which would increase workload.
I assume that the mil use QFE because they like it and the controllers can provide some separation. Don't forget that anyone bashing circuits at a civilian airfield will use QFE.
If the mil want to transit civil CAS then they will be instructed to fly QNH for separation purposes. I find it far easier, with less workload to use QNH, 1013.25 and airfield elevation.