I don't think a lot of games could work like this and thus far you guys are not making a case for it being particularly plausible and I'll explain why. (oh and I like lists it makes it easy for you to argue any particular point without arguing everything.
1. Lets start with the basics. Most of the work that goes into a game is going to be a part of both multiplayer AND single player. Call of Duty is an example a lot of you are throwing about. The physics engine, the graphics, the weapons all that stuff is going to be in both. Sure there are some unique things in the multiplayer and some unique things in the game but the reality is I'm sure that it wouldn't be worth it economically to split it into two separate things.
Can you imagine trying to separate out the single and multiplayer in any fighting game? Or racing game or pretty much anything other than Call of Duty and getting worthwhile results?
2. Call of Duty and similar games aside where the real question should be do you have enough new content for the multiplayer to justify this or should you just be charging me for some DLC for this game I already own, the Single Player serves as a tutorial. Once you've beaten Starcraft your just good enough to understand why you lost when you go online. Lets be honest here though if you tried to learn Starcraft online you'd be almost every game before you figured out how the tech trees worked.
3. League of Legends IS NOT AN EXAMPLE OF THIS. League of Legends is a free game where you are able to purchase things for convience and cosmetics. There is no single player (unless you count fighting the bots) no campaign mode. You can earn IP to buy your charachters just not the skins and even if you never give them a dime you have access to whatever charachters are free that week (or that you've purchased with IP) you have access to every map available as well.
League is a brilliant plan and I'm sure they are making a boat load of money, anybody who plays the game can tell you that there is a point where if you haven't bought at least a skin for your main that maybe you don't actually like the game.
4. I think a much stronger case can me made for perhaps a directors cut or something similar costing extra. CoD:MW2 only had a single player because ancient law demands it. It was short, real short. I would happily have paid and extra twenty bucks if they would have made the game a full length game maybe fighting some of the same battles but from different angles or something, anything.