I think part of the attachment to a club comes from the sheer number of them, everyone has a local club in some division. I mean in London, which is obviously a very large example, but you have Arsenal, Tottenham, Fulham, Chelsea, West Ham, QPR, Crystal Palace, Millwall, Charlton Athletic, Barnet, and I'm sure at least one I missed that are professional. Granted they aren't all in the Premiership, but they are all professional clubs that have followings. Just think about England, there are about 100 professional clubs in that small area. There are only 30 teams in an American sports league, give or take a couple, spread out across the country. Like, for instance, I'm from Indiana so obviously I support the Pacers and Colts, but I could easily choose any baseball team, I'm fairly equidistant from Cincinnati, Chicago, St. Louis, Cleveland.
As far as a draft, clubs have youth teams that start at a very young age. I know in England a player has to live a certain distance from the club to be able to play for them until he is a certain age. This can be circumvented by the club buying a player's parents a house or the like, but I dont think its that often abused until a player turns 16, when he can sign a professional contract.
Where the big clubs have really gained is with the advent of a worldwide audience and merchandising, obviously people around the world want to become a fan of a good club. You can call me a glory hunter, bandwagoner, whatever, but if I saw an English person who chose to support the Royals or the Pirates, I would wonder why he choose them. This has enabled the big clubs (Arsenal, Barcelona, the like) to earn so much more money than the teams that don't have quite the worldwide fan base.