None of those things were said/done over social media—I could be wrong about Obama here. All of those statements and actions were covered by the media because they were newsworthy.
Some of Trump’s tweets are also newsworthy, of course. But the format of direct communication without context to millions of followers is a big part of how he was able to spread and maintain such a false view of reality.
Before, any statement from a president was reported on, and usually presented with additional context that includes fact-checking where possible, by a broad range of left- and right-leaning news outfits. That’s no guarantee that batshit-crazy lies don’t get through, as we saw with Iraq WMDs. But it generally provides better safeguards. Trump can still call a press conference, or even put out videos from the White House, any time he wants to. It is not a hardship. I’d argue that he liked Twitter precisely because he controlled the information, and could rely on people to take him at his word.
I realize that I’m painting kind of a rosy picture here, since so many trump followers already hate and distrust the media. But presidents got by without Twitter before trump and if it came down to it, whitehouse.gov is just as easy to check for new statements that aren’t edited by the MSM. And I think this is too little, too late from Twitter as well—they never should have made a separate set of rules for him. I don’t think your “future historical records” holds water here, since every tweet he’s made is already archived elsewhere, unless you were getting at something different.
As a similar thought exercise to yours, if in the administration’s view the election was stolen, that surely counts as a national emergency, which qualifies the president to “tweet” whatever he wants over the emergency broadcast system. There are plenty of other avenues he can use.