Kind've, kind've not. If you're a government agency and you employ a new staffer outside of PR, you're not expecting them to tweet stream-of-consciousness. Trump, on the other hand, was largely elected because he did do this and it's expected of him.
I'm first in line to criticise the primitive Electoral College, the cancerous state of US gerrymandering, and the vapidity of the two-party tribal system, but voter turnout was high. Bush and Gore each got 50M votes in the 2000 election. Obama/McCain was 70M/60M (also: McCain's loss was much greater than Trump's). Clinton/Trump was 65M/62M. Unless Trump's numbers were rapaciously Russian-ified, he still put in a solid showing with voluntary voters.
Trump's appeal was his unorthodox, un-polished dog-whistle politics, and his faithful lapped up his 'tell-it-like-it-is' approach, even if the 'like-it-is' part was fabricated out of whole cloth.
Also I don't think it's particularly ironic that the President of the United States gets certain privileges which his subordinates don't.
That part of the "shutdown" was rolled back once the issues were understood, but in the interim those kinds of Twitter feeds were pointing people to their Facebook page for up-to-date information. I guess we're lucky that no one included Facebook in the shutdown order and even luckier that there was no relevant emergency while the social media policy was being clarified.
One thing I never do is to completely shut down the app and take it offline while I scour through the code to ensure everything is ok. Not unless there is a glaring problem or security hole that is already evident.
It is ironic that the person giving the orders to restrict his subordinates from tweeting can still continue tweeting his stream of consciousness stuff carte blanche...