marjben--when you just sew long and whack off excess, you are not getting a square quilt. By measuring (either using the middle two measures or by measuring sides and middle and averaging) you are basically forcing the quilt into a uniform shape, which in turn allows your quilts to lay flat.
When you take those measurements you are able to see if there is a problem with the "squareness" of the quilt--whether there is a need for trimming or re-sewing to take in excess. then your borders can be attached so that the corners are square. I was taught a quick way to see if there are major problems before you take your 3 measurements is to fold the top (without borders) into quarters--if the corners don't meet when folded carefully, you have problems! Also I was taught that difference in measurements of 2 sides & middle should not differ more than a 1/4" from your average--which can easily be eased in. Hope that makes sense (although I have to admit when making table toppers, etc I have been known to "whack off excess" on borders!)