I completely understand Yahtzee's point of view on this one, although my own does differ.
I have been playing a LOT of multiplayer games over the past year, whereas before i avoided them, playing single-player games and sandbox games almost exclusively. I found the competition to be exhausting at times, you have to be on your toes and alert all the time, and that isn't why most people play videogames. If gaming is a form of relaxation, as it is to some people, then being thrust into a situation where you're stressed is the opposite of what you want. Recently i have been playing a lot of Halo Reach and a lot of EVE Online, in Reach i am often frustrated at the lack of coordination in my team, people who seemingly have no idea what our objective is, or that they are infact part of a team that they seem to be ignoring. What changed my mind was the rare moment where, together, in a perfectly orchestrated move, we pulled off something spectacular, in that sense the game ceases to be mindless competition, and becomes a "co-op" experience, with people working together as well as fighting eachother, if that makes sense...
I do prefer coop to competetive, i enjoyed Gears of War and Army of Two, the old Operation Flashpoint, games like Halo and Resident Evil 5 for that very reason, i like working with friends, or even strangers online, as long as we can work as a team.
In EVE there is a very tight sense of community that i really enjoy, it's very alien to me to actually enjoy the company of the people i'm playing with in any other context than that of the game, i often find myself just having conversations in the chat window while i'm docked. When you actually go out and fight alongside these people, the feeling is great, and if you succeed you can all celebrate together.
While we're on the subject, i'm kind of pissed that the games of our current gen RARELY have coop modes, in the PS1, Dreamcast and PS2 eras there was never an FPS without some kind of split screen mode.