Soccer (what the rest of the world calls football) might be the big thing in American inner cities, as like basketball it requires very little equipment.
I'm not sure about this. American football is extremely popular in inner-city U.S. neighborhoods and requires a ton of equipment. That equipment is supplied by the schools whose teams they play for. I don't think the popularity (or lack thereof) of any particular sport comes down to the amount of equipment needed, at least not in any Western country. Most sports have modified forms that you can play (like touch football) that get around that problem. The popularity of a sport comes down to cultural factors. Soccer just has never really caught on among inner-city Americans. Maybe it would have without basketball, but I'm not sure.
Also - just a pet peeve - it's not true that the rest of the world calls it "football." Much of the English-speaking world (including Canada, Australia and New Zealand) calls the sport "soccer," as do French Canadians. And Italians call it calcio.