I think it only really applies to clearances of a certain length that contain quite a few bits of information. I occasionally say "correct" when doing ground having given quite a complex instruction, and certainly always do when passing route/departure clearances. I'm not sure of the exact psychology behind it, I think it's a human nature thing. If you had a conversation with someone like this:
"How do I get to the train station"
"Straight down there"
"Straight down there, thanks"
Then that's fine. However:
"How do I get to the train station"
"Well you turn first left then all the way to the end of the road, take the 2nd exit of the roundabout and then half a mile later you'll be there"
"Ok first left, end of road, 2nd exit and then half a mile down."
... The other person has to say something at this point to conclude the conversation.. so "Yep that's it" happens.
So perhaps it's something that just stems from our communication culture!
The MATS 2 here says that you do need to say "readback correct" when doing departure clearances.