For the sake of accuracy, I don't know how long ago Corporal Motors disappeared but ICAO only changed from mB to hPa about five years ago.
As to the UK MATS Part 1, I guess it gets quoted a lot because a lot of the contibutors to this site are from the UK. You're right that it should all stem from ICAO, as modified by each country.
But I'll vote for the MATS 1 over Doc 4444 anytime because it gives far more interpretation and guidance.