See, your problem is that you play League of Legends. There's big issue number one...the game claims to be team-play friendly, but when half the cast of heroes can qualify as a carry, it means there's no reason to play as a team. Everyone's busy thinking, "No matter how hard the other guys on my team screw up, we'll win as long as I get my items." Why play as a team when it's literally way more rewarding to just pick a carry and farm that shit up?
Now, if you played something a little nicer, like say Heroes of Newerth, where a team full of carries is a great way to lose in under 25 minutes, you'd have to have more teamwork. Problem is, people who play Heroes of Newerth are even LESS friendly, and playing it is a damn sight harder than League of Legends is. Also, you have to buy an account, so it's not free. So, well, guess you'll have to choose your battles.