IMHO the main advantage of neatly loading dishes neatly is that unloading becomes a 60 second exercise as opposed to a 5 minute one. It's not so much that I don't have 5 minutes to spare, but my back appreciates it if I can get it done quicker. I get 4 plates with each hand, silverware is already sorted neatly... it's just overall a better experience.

In other words, even if you believe the time taken to sort is identical whether you do it loading or unloading, the difference is if you do it while loading you divide that task into many smaller tasks instead of doing one big sorting task on unloading.