The line of logic you put forward does seem agreeable too. Mind you I do then have to read picking sportsball team then gets to be a function of laziness and some kind of localism (if that is even a term), though I am a great advocate for the former the latter always feels distasteful.
Unless you produce some hard, wide-ranging polls, then we really don't have sufficient info to determine why each of the like 200 million people watching the game roots for whichever team they root for, if they root at all, or are even fans of the teams, or football in general. Your train of thought only works in a vacuum, in the real world there are dozens, perhaps even hundreds of reasons someone roots for the team they do.
I root for Boston teams because my family would get together and listen to the Red Sox on the radio, or I'd sit with my grandfather in the den and watch games on an old tv. Some of my fondest memories are watching the Sox when they had losing seasons. As I grew older I could have easily picked another team to root for, but what should the criteria be? A team's logo, perhaps I enjoy a player on the team (this is actually why I pull AC Milan, because I'm a major fan of Honda). It's all arbitrary in the long run anyway, just as some would say rom hacking is, that doesn't mean it's any less enjoyable, or exciting to me.
I assume I get the same amount of pleasure out of sports that you get out of building things in the shed. I may see engineering as nothing more than a pure application of logic, whereas you may get emotionally invested in said projects. The reverse is true for me and sports. Sports around here are more than just the games, they're about socializing, cheering with friends, being down after a loss, getting hyped, and amped up etc.