My guess is that the US used to have objective criteria but because University admissions are so competitive everyone studied just for the test and Universities filled with people who were very good at "book-learning" at the expense of everything else.
They wanted students to be more varied, more well-rounded individuals instead of robots who memorize books. So naturally, they started testing for holistic well-roundedness and Goodhart's law did the rest.
I heard something similar too, that Harvard felt they were admitting too many Jews so they started using other criteria instead of just the written tests for admission.
Now they are probably using the subjective tests to attract disadvantaged minorities.
They wanted students to be more varied, more well-rounded individuals instead of robots who memorize books. So naturally, they started testing for holistic well-roundedness and Goodhart's law did the rest.