Over here in Germany some city administrations won't do such things for money, but to make sure that this is not seen as an official page where false information is spread. Finding the right balance can be hard. I would assume it's the same over there, rather than actually trying to get money.
People look to Facebook as the effective channel for anything. Unofficial fanpages of stuff are usually significantly more informative and up-to-date than official ones.
Example from my city - the best way to find about problems with public transport (e.g. a tram had an accident and blocked off an entire route in both directions) is through an unofficial Facebook fanpage.
Wouldn’t it be simpler to ask the pages to politely put in a disclaimer saying they are not affiliated with the government rather than threatening damages or shutdown?
And yet your bank doesn't need a special law regulating the use of its name. We already have laws against fraud, which cover such misleading cases. This is much more broad.