Typical (and safe) dominance is mad feeler wars, pushing, chasing, and posturing.
Potentially deadly dominance is grabbing, riding, or pinching.
Yeah, in the wild hermit crabs will work things out for themselves. But they also have the option of running far away if they encounter a crab who is being very aggressive. In our tanks they are forced to share the same spaces for food and water, and are in close contact during down-times and molting. I think it's best that we step in and try to prevent injuries or worse from occurring when we see the warning signs.
With new crabs, it's very rarely true dominance. Rather it's more like survival strategy. They're starved, so they don't want to share or compete for resources. They're new and weak, so they're wary of strange crabs who may get the better of them. They don't have the best shells in the world, and their nature dictates that they do whatever they can to get a better shell that will protect them better. In the wild hermit crabs form chains of crabs that swap shells when one new shell becomes available - it takes new crabs a little while to realize that there are always new shells available in our tanks and they don't have to convince or bully another crab to switch with them.
All of those things can usually be overcome by a brief stay in isolation with lots of food and water, and new shells to move into. Once they get a full belly and a new home to carry around, they become much more relaxed and pleasant. I've noticed that just three days in heaven is enough to get most new crabs into the happy colony spirit.
Also, a bath before introductions will help smooth things over. Just the new crabs need to be bathed in fresh dechlor water - that seems to let them understand that the current crabs are the boss, and it masks the smell of the new crabs from your current crabs so they have no idea that there are new members that have joined the ranks.