The basis of MOBA games is a mismatch that will exist in spite of the skill and effort of any one player. This characteristic, to my thinking, is the reason for their popularity and existence. The human being's high level of response to random reward schedules as opposed to fixed rewards is why this gets such a high response.
Back when I was playing Warcraft 3 prior to the the momentum of DotA allstars the most common game-type was the basic, ladder style competition of Warcraft 3, the RTS. In that game, the bulk of which being played as 1v1 and 2v2, each player had a very direct reward of winning and losing based on individual skill and effort. Once DotA allstars came on the scene, players flocked to it for the chance of going 20 kills and 2 deaths with little to no opposition and the fact they only had to micromanage one powerful hero. Sure, the very unskilled DotA player probably won't stomp an entire match very often but it has a chance of happening in a DotA match much more so than it did a Warcraft 3 ladder match.
The surrender option exists to save players on a disadvantaged team from the very design of a MOBA game. Dota 2 opted to not allow players to quit under any circumstances; instead adopting the maxim, "Stay right there and take the punishment for the next half hour so that someone else can have a good time. Eventually the roulette wheel will land on you." MOBA games are far less balanced than other game types that don't have a buildup of stats and items making one opponent greatly advantaged. I would much prefer to seek the matches that exist in that narrow grouping of "even match-ups" and have the opportunity to opt out of those matches that clearly aren't that.
On another note, as someone who has played a fair bit of LoL, I have to ask how often are these surrenders occurring? After reaching max level and mixing in some ranked play with standard games: the number of games ending in early surrender have been, for me, around 1 in 8. Large mismatches and surrenders occur more often when I queue with less skilled acquaintances. I regret the implications I am about to make, but I have to ask: are your friends making a legitimate effort in these games?
Quitting is a time honored staple of pragmatism. Here's a very good song about this idea: http://www.youtube.com/watch?v=CK71zjFc_yw