Baseball, rugby and soccer

I am writing this article a couple of days after visiting the world-famous Fenway Park. This was my first visit to any Major League sports event in the USA, and it was as good as you would expect. The game was close, the view was excellent and the atmosphere was wonderful.
And though I am English, and though baseball is played routinely only in Canada, the USA and Japan, I am not about to bash this sport.
I may write in the future about the nature of the major leagues in the USA and Canada, compared with the more 'free', less commercial leagues of the rest of the world, but I am not writing about that today.
No, this post is about team sports.

Baseball has a team of players, but it is not a team game. At any one time, there is a pitcher and a batter and the others on the field are just incidental. I'm not naïve - of course there are other interactions happening - but when it comes down to it, the game is about the pitcher pitching and the batter batting.
For those of you who are not familiar with baseball, previous batters can stop at bases if they cannot make it all the way around when they hit the ball.
And at one point in the Red Sox game against the Tampa Bay Rays, Dustin Pedroia tapped the ball away to make himself out, so that his colleague could run home, but that was the only overt, selfless and team-orientated act of the whole game.
So it is ridiculous to compare baseball and rugby. Rugby is a team game where all the players contribute about evenly to the outcome of the game. The occasional wonder player might score three points, complete a conversion (for two points) or score a try (five points) without much support from the rest of the team, but the team are still intimately involved in every score.
Rugby can be compared with American Football. But can American Football be compared with Soccer (Association Football)? I would argue: no.
Football looks a lot like a team game, but it's a much smaller team than the roster would suggest. At any one time, up to three players on the attacking team may be involved, but rarely more than that. If rugby and American football are the most 'team' of team sports, then soccer is along the spectrum towards baseball. At the other end of the spectrum are golf and tennis...
Do you agree? If you like team games, why would you prefer soccer to rugby? And do you think baseball is a team game in name only?