How important are essays?

Even with coach support at some of the schools you mention, admission is not guaranteed. I cannot imagine submitting an application, including essays, which was not the absolute strongest it could be. Being a recruit is not a free pass to skip the boring or hard parts of college application. For most students, especially D3 applicants, it just means that the hard work pays off with an ED acceptance so the student knows where they are going 4 months before RD applicants.