Anything posted through those means should be maintained as a historical record.

I agree with how Twitter handled it; they made it clear that it was in violation, hid it by default, however kept it.

In my mind, I need to consider a situation as if the president tweets out something that _clearly_ violates ToS; such as something overtly racist, or a direct threat.

As a 100% fake example:

> "I am encouraging the Military to use live ammunition tonight in DC. Anyone out after curfew deserves to be shot on site!"

The fact that this was by the president is 100% important, and needs to be available to be seen by anyone that wants to see it. Anything less is a huge safety risk, and in my opinion, if a platforms removes that content it constitutes gaslighting the public.

This way a private company doesn't decide or is responsible what gets archived/deleted/censored/annotated but it always gets archived using what worked for every document produced by a president for decades.

I think you have a point of it being archived but I think you're wrong about who should archive it. At the moment the president tweets official policy (maybe debatable, but let's assume it is), so those tweets should fall under the presidential records act and be archived by the white house staff. Then it doesn't matter if they are later deleted by whatever social media company, or even if are censored or have a fact check attached to them. The original message is stored and kept. (well, at least in theory)