I am sure it does.
Be that as it may, it does not eliminate any mental gymnastics while doing a Circuit or operating within the MATZ if there is any significant deviation in ground elevation or obstacles with some height.
As you point out, the QFE applies to the landing threshold of a particular Runway.
If one uses QNH, a quick glance as the posted MSA for the Approach or Runway in use gives one a fixed altitude at which safe flight is assured in the specified area to which it applies.
I would assume, while using a QFE setting, one has to make sure the selected height being flown is at or above the MSA for the area one is operating within.
Personally, I would find it much easier working off a single altitude reference but understand some are quite happy doing it differently as that is what they are used to doing.