BB
I'll largely agree with the reply from Easy Street. As to why we use QFE, this has already been stated, but in short it often works better than QNH.
When sat in the back teaching visual circuits I want my stude to learn one set of figures, ie base your low-level, flapless, glide circuit or PFL critical points ALL on height above touchdown. It is easier. My terrain clearance is largely visual/procedural, ie the circuit patterns are based around the local geography. One set of figures are much easier to remember and work every time. Engine failure followed by a possible turnback or ejection, again just one set of figures to think about, especially in the heat of the moment. QNH would make this all somewhat more complex with no advantages.
Whenever I use my kitchen scales (not often!) I could make allowance for the weight of the bowl; I don't. I zero it with the bowl attached to get a new zero datum. I do the same when I check the tyre pressure on my car. 44psi or 3 bar works a treat, but it is actually an absolute pressure of 4 bar. Yes, we could make it harder and do a little extra maths, but why? Within the MATZ we are all on QFE.
Now send me to Luton in my wonder jet and I'll set QNH. All straightforward bar some additional number crunching so I can cross check my alt v dme as we trundle down the ILS (touchdown elevation + 300ft/nm). Approaching DA I hit TOGA and go around knowing I was about 200ft above the runway. In the preceding pattern I knew my vertical spacing from all the other traffic that I could hear on the same freq.
Off now to St Petersburg (okay, I'm now in the sim) and I'm probably back to QFE. Just as well as I also tell the altimeter to display in metres and not feet hence losing me the SA I have gained by operating in QFE.
Back home again, and if I'm lucky enough to be leading a formation display then again I want just one set of figures at each venue = QFE. Gate heights always the same, flypast heights also the same. Just can't afford to be descending to an incorrect altitude - even if it was a simple sum! Frees up some SA to use on other more important aspects of the display such as the wind! Even at a non-airfield based venue I'd like a display QFE if available.
There you go, QFE used when it is most beneficial, but QNH does also have its place.