I actually think essays have the opposite effect. The presence of an essay on an application gives an edge to the student who can bring the most resources to bear in "crafting" that essay. Perhaps, at the extreme, having it ghost-written by a professional college admissions consultant. I'd almost rather it boil down to class rank and test scores. Possibly with the addition of a space for students to list relevant accomplishments in a non-essay format. "First-chair trumpet at state", "state science fair winner", etc. Teacher recommendations are a little suspect as well, since schools (and therefore teachers) have a vested interest in seeing their students admitted to prestigious universities. There may also be students who are qualified from an academic perspective but have failed to sufficiently ingratiate themselves with their teachers. Or maybe their teachers, as a group, don't know how to write "compelling" recommendations (possibly because one of their students applying to an elite university is a once-in-a-blue-moon occurrence).
Also, when it comes to test scores, I'd prefer to see colleges use something more content-related instead of the SAT, which is pretty easily gamed. Maybe something similar to the A-levels in the U.K. or the AP exams in the U.S. If the AP exams were used there would need to be a new math exam created that stops short of Calculus; it's not reasonable to expect every college student to have taken calculus. AP tests are, arguably, harder to "game" than the SAT. In theory you have to actually understand the material.