First off, is it actually true that a modern civil FMS has no dedicated provision for entering QFE? (other than the "bodge" approach of entering QFE in the QNH labelled entry). I've no personal experience of flying an FMS equipped aircraft, being a strictly steam instrument person.
The 744 has a QFE entry in the FMS. However, when using QFE, VNAV and GPWS are not accurate, so VNAV must not be used and the GPWS overrides must be utilized.
Many years ago, I was in a glider club that used QFE for all local ops (the airport was less than 200' MSL). It made sense there (no "sensitive" altimeters), but I still do not see the sense of it for air carrier operations now.