I think there'd be a problem with getting a "White Knight" in the same MRR range as the rest of the game. Even if this were taken into account, what benefit would there be for the player? You don't get to pick what champ you get, you don't get to have any say on how the game is going prior to joining. You will probably be joining a losing team that's getting steamrolled, is raging/salty, and likely has a huge disadvantage in objectives and/or kills. Why would any player chose to join that over starting a new game - unless you really hate laning phase?
Additional problems - runes/masteries/summoner's are all determined by the "summoner" before the game begins. Would this "White Knight" be taking over a champ and using their runes/masteries/summoners (and how would that work in terms of the game interaction) ? In game items would probably carry over - potentially resulting in the white knight having a crappy build in addition to the other problems.
It sounds like a great idea - I've had games where my team was winning and someone's internet died or they had to go, etc, and we could not close out the game 4v5. A player coming in to save that would be wonderful. However, there have been maybe 5 cases of that sort of problem in my games over the past 5 years. There have been many, many more times where someone rage quits and there is no hope, regardless of if another player joined.
So while it sounds nice and might actually help 1% of the time, the vast majority of games with leavers are unsaveable and there's no incentive for players to want to join that mess.
