It depends on what you think the purpose of the grading should be (and hence, the purpose of the "A").
Presumably, even at Princeton, there is a rank order of effort and ability, from low to high. If the purpose of the grades is to rank the students from highest to lowest (within the universe that is Princeton), then giving them all "A"s defeats that purpose.
These exams at Princeton are not qualifying exams, like medical boards or a bar exam. It should be possible, if the examiners know the material, to rank every student, by letter grade, from #1 to n.
I dispute that this premise will necessarily occur, especially the higher and higher you get. I believe it is possible to get a group of hard-working students of roughly equal ability who want to learn.