Also, you have now incentivized zero sum competition within the cohort or finding a weaker cohort to beat.
I have met plenty of people that went to top 20 schools that just gave up once they got there yet, still managed to graduate and go to graduate school. I have met plenty of people from my undergrad (definitely not a top 20 school) who were absolutely relentless in their studies and managed to have far more lucrative careers than those slackers who went to top 20 schools.
I mean, I have nearly 3 degrees in EE, CS and Physics.
Physics is usually one of the hardest majors at any university and my homework assignments/tests weren't much different than MIT's homework assignments/tests; sometimes they were a lot easier and sometimes they were on par with their graduate classes. For my lectures where MIT had their OCW version online, they were near identical; the lectures where there wasn't a corresponding OCW lecture, the quality was around the same. Moreover, CS and EE weren't much easier than physics so I can't imagine top 20 universities had much higher quality there either.
(My university also deflated grades to the point where the average GPA was a 2.7 which made it that much more cut-throat (since a 3.0 was the cutoff for many engineering jobs))
(Also, from what I recall, UCSB was much harder to get into than my school yet, they were blacklisted at many engineering companies for having the earned reputation of being a party school; while, at my school, we had those companies consistently come to our career fairs)
If idiots manage to graduate top 20 schools and yet idiots of similar caliber can't graduate from schools that are far below the top 20, their grade inflation is completely unwarranted.
And if we adjust Chem majors according to the grades of Chem majors then small majors, with a high standard deviation, would have greatly different adjustments from year to year (and at my school there are many majors where the numbers of grads in a year is less than 10).
I did not meant to imply you would average letters, they are just the usual way to express the grade.
Yours would put students at schools with other good students at disadvantage against those who go to less competitive schools.
The assumption that students in different schools should have the same average is likely wrong.