Without getting into the whole rabbit-hole of monopolies/government good vs evil... Do you see any realistic alternative to an auction allocation system for mobile frequencies?
Rather than have a tiny band for each company you could select a protocol for each band and let companies freely compete based on which has the lowest cost and a clear signal to each cellphone. Thus making it reasonable for 3rd party's to for example add a few towers near a convention center.
Unlicensed spectrum works extremely well for low power devices that don't cover long distances. If your roommate is using too much bandwidth you can hash it out together. The problem with using it for high power long distance frequencies is you get tragedy of the commons pretty much immediately.
It would be interesting to try for the midrange though. Provide unlicensed spectrum at power levels that could cover e.g. a street rather than a city. Then you could get very local ISPs: One person on your street bites to bullet to buy a fast leased line for $$$ and then sells internet access to all the neighbors over wireless.
Maybe lottery? Though unless you had some restricitions on entry that might just result in the winners reselling their allocations to the established players for a profit.
Auctions are a superior solution to lotteries from an economic theoretical point of view. No point giving spectrum to a company that can't use it properly.
Lotteries have been tried, and yes, it did lead to all kinds of work being done to be able to enter the lottery multiple times, for people to enter the lottery just to resell, and other similar shenanigans. More here: http://www.nytimes.com/2013/06/05/business/in-wireless-spect...
So a lottery quickly becomes a special kind of auction where lower bidders still have some chance to win.