Can you imagine the complexity imposed in a country the size of the UK by flights transititing ASR's within airways with differiing regional settings - not to mention turboprops or perhaps a day where the isobars are tightly packed.
FWIW because of the high TA/TL in the States and the complexity of some of it's airspace (especially the Eastern seaboard around BOS/New York/PHL/IAD) it's not unknown in the descent to do pretty much what you describe - to fly part of the descent, including STAR altitude constraints on one altimeter setting and then have to change setting when handed over to the next agency to continue downwards, eventually landing using the airport "altimeter"....not pretty but you just need to be ready for it.