This is called film cooling, and SpaceX actually does use it on their second stage engine, the Merlin vacuum variant (MVac). You can see the beautiful exhaust plenum wrapping around the nozzle [1].
This isn't used for the regeneratively-cooled portion of the nozzle, but for the large radiatively-cooled nozzle extension, visible here [2].
This isn't used for the regeneratively-cooled portion of the nozzle, but for the large radiatively-cooled nozzle extension, visible here [2].
[1] http://imgur.com/HvtBYIi
[2] https://i.stack.imgur.com/9qIFO.jpg