[bjwbell]

Considering the completion rate for PhD programs, admitting a broader applicant pool would likely make it worse.

[daniel-levin]

Or better, because it is possible that the current process selects adversely.

[barry-cotter]

If you go to Google Scholar and look up the correlation of GRE score with completion, publications and professional success it will be positive. The fact that it isn't predictive within a programme is just a reflection of range restriction, same as how Google found that GPA had no reliable relationship on job performance in the set of people they actually hired.