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 ). I'd like to go back to Cynosport with Gusto in a few years, and if he does as well there as Meg did with her stopped contacts, I will be over the moon!