At this point the officer has no means to communicate with, observe, or give papers to Hill, and chooses to violate Hill's dictate and knocks again on the window. The officer loudly states: "Keep your window down." Hill slightly lowers the window and states: "Don't tell me what..."
At that point it becomes hard to follow what is being said but at 1:45 of the video the officer instructs Hill to get out of the car. There's some argument that's hard to follow, and at 1:51 they apparently open the door (I was shocked it wasn't locked). I'd agree that a de-escalation situation here is possible as Hill clearly realizes his act has been called and pivots from ordering the officers around to being in victim mode.
The video you linked states, in Terry v. Ohio, that inspecting the driver's license, automobile registration, and proof of registration, and attending to safety concerns are part of the officer's "traffic mission". It seems pretty clear cut that is the longstanding precedent that justifies their actions during this stop.