There are multiplayer modes/games that can and can't be runned. Most of them can't but some have running potential such as the co-op adventure mode in Uncharted 3 which would make quite good for runs.

That is just ... why? The "Run" is completely random. PvP isn't made and doesn't work out as Speedrun, simply because it can be manipulated very easily. Just image, that one of your buddies is in the enemy team and gets killed by you as often as possible, so you can get more EXP. That is just one possible way to manipulate it. The other thing is the consistency and how long you're gonna be able to "run" it. If you start to "run", for example your CoD in the BEGINNING, so when it's getting released or at the XMas sales. There're gonna be allot of beginners, which allows you to get way more EXP than later on. Another thing is, how LONG you're gonna be able to run it. Think about running the Game in ... 2026, so in 10 Years. What do you think how many people are there going to be that are gonna play such an old CoD. Maybe ... 100? Good luck finding a Game there, since they will be scrambled all over different Gamemodes again.

And all of these things don't only apply to your Game, but to all Online-PvP-Games. Way to random, inconsistent and no insurance that it's gonna be runable in X Years.