We have a chain of command in our government for when people die. First the President, then the Vice President, then the Speaker of the House, then the Secretaries in a predefined order, and so forth. Plus, the Secret Service (which protects the president) includes considerations for, say, Nuclear Bombing of the capitol and who would take over leadership if such a disaster should happen.

If the rioters had succeeded in murdering every single person in the capital building, there would have been a protocol in place with the leader already determined. The only way this would have been successful is if the rioters killed every single elected official and secretary in the building, followed by having the support of the Army. They were absolutely nowhere near that.

Yes coups require explicit support of the military and/or populace. They had neither.