I think Max Angle has made a very valid point. Once we have cleaned up all the obvious mess from our own flying duty, there is still a lot of ongoing grime (dead skin, fluff crumbs and dust). This would be present in any work station including the MD's desk. The MD's desl along with those of her minions will of course get cleaned properly at least weekly if not daily.
Our company doesn't even seem to be able to find an aircraft cleaning company which owns a vaccum cleaner. There is little chance of an improvement.