Even if everyone agreed on a standard and its impact on admissions (+3 for participation in the Model UN, for example) it's not clear how we'd judge "better results" as we evaluate our admissions criteria. Are we optimizing for an even racial/religious mix of students? Higher output grades? Higher wages? More children raised successfully by the age of 40?
Then even with an agreed upon goal and some objective measures to used to approach it - is it worth doing? If we could get 1% better results by doubling the difficulty of the application process for the students then it probably wouldn't be worth doing it when the plan was considered holistically. What's an acceptable trade-off? What's the cost on transparency and perception of bias when we start considering subjective criteria?
Of course, the process is still a far way from random.
When I last looked at the research many years ago, other signals certainly tended to be noisier but there's no particular reason to think that admissions would be better if universities simply set a test floor then rolled a dice.