I've been in the position that the original poster talks about where your teammates don't even wait for the others, but as each one respawns they rush out to the lanes where they quickly die in 3v1, 4v1 or even 5v1 fights. You can of course go to make it a 3v2 or so, but that just means you are going to get to watch the countdown timer as you will be killed quickly.
So you end up in a bad situation. The fight is effectively over unless your team happens to get all 5 members up at the same time and win a teamfight somehow, but that will only happen if your teammates stop charging to their deaths.
And often the only reason the game is continuing is that the other team isn't actively trying to end it. This is something I've seen more than once, where a team that is clearly dominating and that has several well fed champs decides to keep the game going since they can get a lot of kills. The game can be extended 7-10 minutes by this process, which again is just frustrating for someone who is not interested in being a practice dummy for a fed team.
There is no simple answer here. I agree that there is no reason to just die again and again in a bunch of pointless fights where you are outnumbered and just feeding already well-fed champions. There should be a point where your teammates recognize this and won't report you for saying "I'm done dying in a lost cause." At the same time there are many LoL players who are far to quick to declare a cause lost. If we can find the right point, then we can perhaps fix this problem. until then, all I can recommend to the original poster is that he needs to at least try to support his teammates in their quixotic quest to win a 1v5 teamfight, and avoid looking like he has completely given up. Perhaps he can do something to help the rest of the team get organized. Just turtling in the base won't win the match.