How important is it to visit each college and network with the admissions reps?
Would you get married without a date? Would you buy a house without visiting with a realtor? Of course not. Neither should you apply to college without visiting, to determine whether its programs, physical campus, and student atmosphere are a good ft for you.
In addition to helping you decide if you can picture yourself at this college for the next four years, it is important to visit to demonstrate your interest to the college. Admissions people need to predict yield, and it is important to them to be able to guess whether you would really enroll at their school if they were to offer you acceptance. If you have visited and interviewed at the school, and you mention this in your supplementary essays, admissions will realize there is a likelihood you might really attend their school if accepted.
You do not have to "network" with admissions reps. But you do have to visit, and let them know in your application that you have done so.