Just to back up what Athene says wake is from nose up till nose touchdown.
We do give take off clearance before the 2 or 3 minutes are up on the basis that generally take off roll takes about 30 seconds.
Any pilot can say he/she wishes an extra minute at any time and no ATC will force them off the runway. It's more than our job is worth, especially if that aircraft then experiences problems due to turbulence!
It would be nice if all pilots said they wish extra time before lining up especially when they can see something is bearing down on finals, but this isnt always the case. I know that from a personnal perspective I would rather send something around on finals than try and "force" any aircraft to take off when the captain isnt happy about doing so.
At the end of the day we all want to go home "fat and happy", not have to spend the rest of the day filling in forms and explaining why an aircraft was put in danger!