ATCOs at MME dont sit around doing nothing! Have you ever been there? Just because there are few schedule movements doesn't mean it isn't a busy unit! There are many different problems that controllers at MME deal with on a daily basis! These include the large amount of military movements through the Vale of York (less recently but still busy), the large amount of GA traffic in the area as well as dealing with traffic entering and leaving air ways.
I do believe that it is an advantage to have controllers in the local area, I know its not essential!
On top of this the cost of employing controllers at LPL is alot more expensive than at MME!