Yeah, I really get the sense that working together as a team (especially in shooters) isn't important or really around anymore. I think the Battlefield series is an excellent example of that. Just play Bad Company, and you will see that while people may "help you out" by shooting the guy who's shooting you, but it's not like they're doing it for any other reason than keep their score up. I think that in order for a true team-based game to work is to have more of a penalty for dying because if you don't help your teammates survive, they'll just come back 5 seconds later at a spawn point, so what's the point of helping them out?
You can always try a sports game lol
If I die today, I'm happy how my life turned out