Rule 3-1-2
 

Looking at this rule it states any player may request permission to leave the court. When would this situation happen? I couldn't think of one. What is this rule talking about or trying to address?

Here's One Example
 

Had a player approach me in apparent distress, signalling with pointed finger towards the locker room, cheeks bulging from obvious internal pressure.
I gave him permission to leave the floor so that what he had built up he would not leave on the floor.

Since they're not allowed to change jerseys on the court they could also need to request to go to the locker room to do so.

I don't know that I've ever been consulted to get permission for a bench player to leave the visual confines.

Me either, especially if it's to change a jersey that's ripped or has blood on it, but that's a scenario I can imagine happening in response to the OP.

A player is one of 5 team members on the floor. A substitute on the bench is not a player and would not ask permission to leave the floor since he wouldn't be on the floor. :)

My guess is a player with a torn jersey would ask his coach for a substitute as opposed to asking to leave the floor.