At the Jiyushinkan we line up for formal opening and closing of class in order of rank. Some koryu dojo we train in do it in order of seniority in the system (this has nothing to do with "rank").
The person we train with has nothing to do with how we line up. Seniors are expected to train with juniors before they train with each other. Seniors usually take the role of uke first to set the tone of the training.
I, personally, see rank as a sign of skill and leadership responsiblities. In the Jiyushinkai, rank is handled in ways that are similar to our koryu practice. Teachers determine when someone is promoted, not a board of people that do not know the person. Our promotion board is tasked with keeping technical standards at the level they should be throughout the organization. Promotions above sandan must be approved by consensus of the promotion board. We do not do tests. Students give a public demonstration so they show the nature of their practice to everyone. Juniors can see what they need to accomplish for a given rank. This also gives the instructors a way to evaluate what they need to work on to get things across better.
When a student is promoted to dan grade, it really is both recognition of accomplishment and a promise between teacher and student that goes both ways. It is recognized by those that take part in our system. Some people outside our system respect our grading, others do not. It is the way of things.
Rank is like a Zen koan that needs to be worked through. It is important and yet it is not important. Each person has to struggle at different levels with this conundrum.
At some point, what is important is how we view ourself and then how we share that with others.
As Kano Jigoro-sensei said, "Best Use of Energy with Mutual Benefit."