I can understand how people perceive that a sport has to be longer-match based. Most of the dominant sports in the world are match based. However there are many sports that involve multiple matches per event/day.
Sure football, hockey, American Football, rugby are all sports where just 2 teams can turn up play for an hour to play then fook off. But what about sports like fencing, marshal arts etc. They are on a scale more similar to ours, a large number of competitiors congregate for large less frequent events. The events need people to have an atmosphere, and in the absence of fans lots of competitors will do.
Having the carnival events is a perfeclyvaild way of doing it. I a sense it is similar to tennis, large tournaments drawing in lots of teams for several matches. Admitttedly these are over several days. But you might just as easily critisze them for there large events and lack of league based system.
Having said all this I can see the attraction of an Xball league though, have divisons of say 30 and everyone plays everyone else once over the course of the season, turning up once a week for a match.
It could also be done in a way similar to sunday league with each team having to have its own pitch, and having home/away matches. A central pool of refs comes out to each event to ref. Of course the problem with this would be coverage, it would be a nightmare to film, or even photograph the matches, as they would be all over the place.
I've always thought that the way to get attendance at a national league would be to have a touring national league held in the evening after local tournaments around the country. Eg the first weekend of every month is the midlands local league. In the evening, the teams get a shower, stow there gear and grab a seat in the grandstand to watch the pro league. The Pro league would play weekly, each week in a different region after that region's monthly tourney. Have southwest, southeast, midlands, and northern/scottish regional tourneys. Set up 4 kick ass venues, with a whole load of fields and one "centre court" stadium type thing for the pro matchs in the evening. Showers, secure parking, pro shop, bar.
And then he woke up and it was all a dream........