I don't use postponing myself, but I can see that one benefit would be that you can setup a Smart List to show you the tasks that have been postponed a certain number of times.
Also, I guess, it's just one click to push a task off to the next day; it would take more clicks to change the date.

Personally, I just change the date if I want to do that. Or, I'll just let it sit where it is so it's showing as overdue. That alerts me to something that I need to take care of.

I'm not sure that helps much. Perhaps those who use the Postpone feature can reply with how they use it.