The problem, though, with not using the GRE is that there is really no other standardized way of looking at academic potential. Sure, it's FAR from perfect, but when used as a tool, it can be useful. GPA is a great predictor, but a 3.8 with easy professors at one school vs. a 3.7 at tougher school with tougher classes should give the 3.7 an edge but how do you determine that difference?
Additionally, every combination of school and individual circumstances is going to offer different opportunities for research, etc. For example, if you have done 4 publications over the course of 6 years of research experience, including getting an MA, is that really any better than a student with 2 years and 1 completed publication and a couple of others "in progress"? I would argue that the student with 2 years has probably been more productive overall (because s/he got publications going more quickly and has just begun).
For those reasons, while I agree the GRE is far from perfect, it is WITH the GRE that we get a +0.50 correlation (GRE + GPA). W/o the GRE, we're left with a +0.40 as I recall. Ultimately, I would consider the General GRE, Psych GRE, and GPA as useful tools in the initial screening of applicants so that more time can be spent on those most likely to succeed. Unfortunately, that does mean some potentially doable applicants may not get in; however, if someone is truly unable to learn the necessary skills to attain at least a 550 or 600 on both sections of the test, I would, to be totally frank, have to wonder how that person would do learning to think like a scientist, speed-reading journal articles for content, and so forth. An 1100-1200 should be attainable by most anyone who was able to graduate college as most of the verbal questions at that level use words and text that are extremely common in college textbooks and the quantitative skills at that level contain very few "tricks" -- most of it is just simple math that we all learned in like 10th grade and had to do on the SAT/ACT and/or in our college alegreba/math class.