I think I am in a very small minority about this, but I feel the edge with a finger or thumb. When you get really used to doing it, it conveys a lot of information, on the order of “this part of the blade isn’t as sharp as the rest” or “I thought I was done with the 3000 stone, but this doesn’t feel like a 3000 edge; something’s wrong, time to pull out the microscope or just keep going.”
I should emphasize how gentle and careful you have to be when doing this, and how tiny any motions along the edge should be. Also you don’t want to keep doing it in the same spot. If I’m doing this on the finisher, I always go back for a dozen light strokes afterwards, just in case I disrupted the edge.