But, once the municipality is done with the fiber, then running the service is "relatively easy." Since the primary asset you are selling is bandwidth, what would be left to let more than one competitor compete for/differentiate? Service? Possibly, maybe faster setup times, etc. But those are "one time" things only.
I think bandwidth is becoming a necessity and local government can deliver it (for the record, I did not vote for Obama last time! ;-)
If multiple providers were leasing the fiber, they could compete on how they handle the data on the other side of the last mile: how they're connected to other networks (peering and transit), price, oversubscription rates, acceptable use policy, willingness to install caching boxes provided by content providers, what services are included and their quality (dns/mail/vpn/homepage/news/shell).
ISPs here (the UK) primarily use the same physical last mile (along with their own hardware in the exchanges), and often the same backbone infrastructure, but differentiate on pricing and service.
There's also enough money caught up in the retail ISP business that if the infrastructure maintainers failed to do their jobs, the retail ISPs could reasonably compete with them, at least in key markets. This, combined with a strong telecoms regulator pressuring them into developing and maintaining infrastructure, generally works out reasonably well; much of the country, including a lot of small towns, now have 50-70Mbps unlimited unshapedc FTTC for a reasonable price.
Nope, in urban areas it definitely makes sense for 4, 5 or more companies to offer broadband in a single apartment building; in countries where this isn't artificially restricted this is the natural result of market competition. Suburbs are different, but USA lacks competition even in cities that have extremely dense population and huge demand.