You've basically described mesh networks. There are a number in cities across America, but are normally run by enthusiasts.
The trouble is, in dense urban environments, there's a lot of noise to overcome, and if you don't work around that, your network will fall apart. Especially a problem with the coming 802.11ac routers which will crowd up the 5 GHz band that is current the target for backbone links in the wireless networks.
Why not bypass this and go straight to the device? Imagine paying for internet and not being limited to your house. Then you can expand your "work somewhere which is not your home and not your office" options beyond just Starbucks, et al. Plus the more different you are from the current business model, the better; you have a greater variety of ways to sell yourself, e.g. "This Internet Option, for the on-the-go professional who doesn't have time for wires!" or "Comcast wants you to have a modem. Lol, ok, Grandpa. Eyeroll.gif" or even "Gee Honey, you were right about This Internet Option. I never realized how much more alive - and sexy, and free - I feel using my laptop on the backyard swing!" Also you could compete on price (dramatically so!) with mobile carriers, if your network of boxes is, say, at least city-wide. Home, work, and between.
(Sorry about that. I was having fun.)
Well, there main unlicensed bands used by hardware today are 2.4 (Full up), 5.8 (Filling), and 24.1 GHz (Relatively clear). If you want to get into other frequencies, you're going to need to license them ($$$). If you want to work with the frequencies already available, you're going to need to plan a little, since different frequencies have different speeds and penetrance.
Wirless meshs are neat in some aspects, a more guerilla approach to internet for sure, but you're definitely going to have an easier time dealing with bandwidth and noise if you just roll out your service over insulated wires.