I think the main reason we've switched to almost all runnings is because it is SO easy to demotivate your dog with a stop if it's not really carefully monitored. We've all seen the pathetic "creep" down the back side of the frame when it's not trained incredibly carefully. With a running, you'll never have that issue (you just have to balance the leaping instead--but I'd rather have an over-excited leaper than a timid crawler)
More than anything, I think it is important for trainers and students to be willing to figure out what is right for them and their dog. It is one of the things I love best about where I train; everything is tailored to each pair. In our performance puppy class, we have two dogs doing a 2o2o, one dog doing running with a treat thrown, and one doing running with hoops. Meg's competition class has a few dogs doing super running contacts and a few doing super stopped contacts. My trainer has 2 competition dogs doing stopped, one doing running.
Gusto is doing stopped contacts for both his sake and mine. He is a dog for whom speed and drive will likely never be an issue - control will be. He's built great for stopped contacts (much better than Meg, which is why I had originally wanted to do running with her). I like the very defined criteria myself (hello, obsessive dressage rider), and I like and likely need that moment to help my handling! I don't expect to go to Worlds where those 1/10ths of seconds count (and let's be honest, when you get to that point, you early release and fix the issue later