<p>The most important function that SATs and AP tests perform is to set GPAs in context, both in terms of the school and in terms of the individual student. A student who gets 90+ for class work but only 1 or 2 on the AP test may have a bad day. Chances are, though that the class was not rigorous enough. Similarly, adcom will look at the record of a student who gets Bs but in the high 700s on SATs differently from that of a student who gets Bs and SATs in the low 600s. And students from East Podunk High who get high scores on the SATs as well as high GPAs will also warrant a second look.
As for essays capturing the essence of who an applicant is: perhaps they do if the applicant was the sole author of the essay. And perhaps they also hide the assistance the applicant had in crafting the essay. Adcoms have no way of knowing which is which.</p>