A lot of pressure could be relieved if ANY certified mx facility could do the work. The paperwork involved to get things going if one wants another mx company to refill the O2 or the like is ridiculous ... at least in Germany.
EASA is in the business of making perfectly simple matters highly complicated and then sticks the head in the sand when operators do "their own regs".
Another point is what is put in the MMEL. In our type we have switches with an "On" and a "Off" indication. They are either flush (when pushed "On") or elevated from the panel if "Off". The manufacturer put that in as a 12 days item - does not make sense and is NOT dangerous in any way, shape or from to fly with one indication u/s... These are going awol on our airplane regularly.
A pain in the butt.