I've been beating this drum for a few years now, and the key point that upsets me is precisely that they
already have their own infrastructure, like you said, but they have practically abandoned those official .gov, .mil, .org websites (leaving behind stale information and dead links) to use Facebook and Twitter instead.
I think this is mostly a problem among small towns, counties, etc. so residents of big cities may not notice it as much (like the death of real local journalism). I think it usually boils down to the fact that it's easier for a lay person to update a Facebook or Twitter page than it is to maintain their own website, and IT people are expensive.
I'm in the US Army, and "Big Army" at the top level does OK with its websites (e.g. army.mil), but it also consists of many geographically distributed, semi-independent, sub-organizations (units) that each have a handful of people doing public affairs work. The official websites at those lower levels have been rotting for years, and public affairs folks have freely admitted to me that they don't know how to update their official websites besides changing the photo and biography of the new commander once every two years.