Great question! There are a number of reasons the schools are reducing the material required to apply and I'll address a main one today.
By forcing applicants to write less, the quality bar of the essays has risen and it is now even more important to get your story across very succinctly. In the past there were multiple essays and eventually applicants got powerful and convincing messages across. It was left up to the adcom to take the time and read through everything to decide what was quality and what was not. With fewer essays, applicants are challenged to convey themselves in an abbreviated format, much like the job recruiting process or the 30 second elevator pitch. With less to write, applicants are actually separating themselves through the essays even more, and so far this approach has been effective.
While many schools are not necessarily using something else to evaluate applicants instead of the essay, they are using different techniques to get a more well rounded picture of the applicant. For instance, group interviews, video interviews, presentations and post-interview reflections are all elements that allow the admissions committee to view applicants from another angle besides simply reading another essay.