I wouldn't call it a 1 man raid, otherwise you'll get straight no's from a lot of people. What I would suggest is "Solo Challenge Modes" of older raids as a way to get some of the removed items back into the game, for example they could do a Naxxramas Challenge with the Meta drakes as rewards or ICC Challenge with a chance to get Invincible (technically this already exists with solo'ing anyway). The difficulty will be hard and like Challenge Modes you have Bronze, Silver and Gold. With Gold earning you the mount for that raid. The raid will scale to your class, and your gear gets scaled to an average ilvl.
This would be a huge time sink for a lot of players, and would promote players to be able to stand on their own feet rather than be carried through everything. Solo'ing is a brilliant tool for learning.