Re: Practice without tradition
When I visted a dojo that occasionally omitted bowing in and out and bowing to partner, I found it personally difficult. I use the opening ceremony as a place to put aside outside concerns and focus for the practice of aikido. Without it, I found myself distracted. I recall spending most of one class fretting about some household issue, and only realizing at the end of class that it was because I'd never made a proper transition to "training mindset."
You could substitute something else for the opening ceremony, but I think that having a clear boundary marker between training and non-training helps lead to safer, more focused training. It seems to reduce the temptation to "fool around" rather than training with full attention.
I also found that bowing to partner helps make it 100% clear which person you're offering to train with; again, you could use another mechanism (shaking hands?) but it's helpful to have something.
There need be nothing particularly "ceremonial" about these ceremonies. In some ways they're analogous to the opening credits of a movie. The credits aren't very important, but if you leave them off people aren't yet settled for the movie when it begins, and don't appreciate it as well--at least I don't. Same with closing credits--they say clearly "This is done" so that people know when it's appropriate to leave, and allow viewers to make a gentler transition back to non-movie-viewing mode.