The fact that the average score for Harvard and similar for other elite colleges for the ACT is 34-35 means that the national average is worthless for the purposes of elite colleges. Majority of people who would even bother to apply for them are basically perfect across the board grades wise, so its worthless to brag about it.

Bar making exams harder, the only other way is subjective methods. I detest subjective methods, but making exams harder is very unpopular

They're not bragging. They're pointing out that the ceiling is dramatically too low, which has caused elite universities to spend decades creating more and more elaborate and more and more detached and meaningless gatekeeping mechanisms. The national average does not matter in the context of the nation's most competitive schools.