As an avid sports fan I've watched many different sports. I think the best way to approach this question is to break it down into types of sport. The largest of these is the grab the ball and run forward type. This involves big musclebound guys grabbing an odd shaped ball and running forward until someone from the other team stops them. The aim is to get past a line at the other end of the field, often there are posts to hit the ball between in order to get extra points. In this category are; American Football, Rugby, Rugby League and Australian Rules Football. Most of these sports can be very entertaining at times although they generally suffer from two main faults. Those faults are firstly their stop-start nature which means there is rarely a passage of play that lasts longer than a few seconds. The second problem is the people who play them. These sports are not pretty to watch, skills are limited as speed and strength are everything. The people who play tend to reflect this fact.
Next up, sports with bats and sticks.
Ice Hockey, which despite having the potential to be a very entertaining and skillful game, is ruined by the neanderthal nature of the competitors and is therefore cut. Baseball and Cricket both have entertaining moments if you've got a few days to spare but best team sport? No way. Hurling and Lacrosse both involve whacking a ball around a field. They're pretty skillful sports and played by real sportsmen. Sadly, the ball is just far too small for the size of the field. Hopeless for the shortsighted.
So, with those sports ruled out, we can have a look at what I'm calling the "randoms". These are sports that don't really fit in the other categories. Football (soccer), Gaelic Football and Basketball. Gaelic Football is an Irish sport which involves running with a round ball and trying to get it past a goalkeeper in a football (soccer) style. It's a good balance of aggression, skill and excitement and the game flows well. Sadly, it's just too random. Players can't just run with the ball, they have to bounce it every few steps, if they can't score a goal, they can choose just to kick it over the bar and still get points. A good attempt by the Irish but bit of a shambles really.
Basketball is exciting, skillful, thoughtful and tactical. It might even be in contention for best spectator team sport if they played it in bigger arenas. Sadly getting tickets for big games is just too hard, ruining the spectator experience.
Which, predictably, leaves football. Simple, skillful, graceful, popular, flowing, majestic are just some of the words that can be used to describe the most perfect of spectator sports. From huge stadiums like the Camp Nou in Barcelona to smaller grounds like Hibs Easter Road, football provides a spectacle that everyone from the very young to the very old can enjoy. It's simplicity, excitement and passion are its strengths.