Who says there has to be. It isn't enough that due to low entry of cost kids can pick up a b-ball and play on the street whenever they want? It's that ease of access that ultimately means more than any number of tailgates.
You can't call it a 'juggernaut' if it's not in the top tier, the most or 2nd most dominant professional league. Baseball was more popular. Boxing was king. The big turning point was television and the late 50s.
I would argue that the ability of fans to "consume" the sport is most important- not the ease of playing it. NASCAR is extremely popular, it has the least ease of access of all sports besides maybe F1 (another example of a sport that doesn't appeal to American tastes). What makes football consumeable can mean many things, but it involves tailgating, the outdoors nature of the game, and football's natural appeal to the medium of television. You'll discount it, but I think the main thing that makes footballl so popular on TV is its ability to generate cliffhangers for commercial breaks. That, and as I said before, its easy to identify momentum swings in both football and basketball. All this makes football consumable as a piece of visual entertainment.
You mentioned baseball and boxing. It's possible baseball and boxing were more interesting when the main way to consume them was through radio. Personally, I find those sports more exciting when heard through the radio (at least I imagine so for boxing by listening to old radio broadcasts of the sport). Footballl needed television to illustrate the drama and strategy involved with the sport- evidenced by the now routine practice of play telestrating. Its natural that its popularity would rise with the introduction of TV.
By juggernaut, I mean unstoppable. While football wasn't nearly as popular as baseball and boxing in the first half of the 20th century, its foundation was just as sound as baseball's, and much more solid than boxing's. It just needed a decent league to support it, and a better way to broadcast its excitement.