The thing that I always liked about Pivotal is that it was visibly obvious that there was only one queue. It forced everyone to ruthlessly prioritize and make the hard decisions. In this moment, do you want me working on this bug, or this new feature? You have to decide - you get one or the other. It avoided the "Everything is a high priority" dilemma.
That sounds more like a disastrous missing feature to me. A good productivity tool doesn’t dictate how teams work. I’d rather have a tool that’s more customizable.
You think you would, until you do, and by then it's too late.
It's important to have good processes, but the point of all those processes is to help you make things more efficiently. Anything that leads to you spending extra time serving the process directly reduces the amount of real work you can do.