Social Media Is Often Beside The Point
Personally I don't think people have trouble speaking clearly or writing plainly when they are free to express themselves. So the problem is not a lack of technical writing skill.
I do think the problem, in government and elsewhere, is the number and kind of formal and informal restrictions on communication. By the time you put normal English through the mill it often sounds like an odd, tortured form of the language we speak.
Formal restrictions concern written laws, rules, regulations and policy regarding what may be expressed and how.
Informal restrictions include unwritten but generally known preferred phrasings or jargon, or cultural sensitivities.
There is also the matter of coordinated communication - because of course the more people involved in the message the less "human" it sounds and the more strained and calculated.
Whatever the kind of organization one is talking about, whether you're selling Domino's Pizza or preparing the public for inclement weather, communication is decided by people with different orientations. All of those people have some say. The conversational types think in terms of how the public thinks - they just want to give a simple straight answer. The subject matter experts think in terms of the complexity of the answer - usually things are difficult to spell out in a single sentence or two. The lawyer thinks in terms of the legal implications of the response. So on and so on.
That is why the whole issue of social media in government is really beside the point no matter how much or how well an agency does it. The crux of the matter is whether the primary communication to the public is clear, comprehensive and credible; whether the issues people want to hear about are being addressed; and whether all communication from the agency is aligned and consistent both internally and where necessary with the rest of the government.
All opinions are always my own.