Let’s take into consideration:
Arthur would rather waste precious time before an important council meeting to run around the entire castle and search for Merlin, who, in his very honest opinion is the worst servant of the entire kingdom or that he had ever known, than to call literally anyone else to help him dress (as if there wouldn’t be anyone ready to assist Arthur, their king, with clothes);
Arthur, and therefore Agravaine (which makes it all the more hilarious) knows every single place where Merlin could be, at that precise moment, or during that day in general; (EDIT: As someone pointed out in the comments, everyone and Agravaine included knows who is the “dollophead”)
The guards nod to Agravaine without asking anything, which only means that it is canon that everyone in Camelot knows Merlin by name; EDIT: It also means that the guards deal with this on a daily basis. They must be tired.
The aforementioned point implies that everyone knows how Merlin looks like, that also means Merlin is known to never leave Arthur’s side, even during council meetings;
Arthur is running around the castle in what today we would call a pyjama, just because Merlin didn’t wake him up with, “Rise and Shine”. And he’s barefoot. That’s right. The king of Camelot, everyone, has just walked barefoot in Merlin’s chambers, in the armoury, where other knights probably are, and in the bloody stables (yes, the ones where the horses and their dungs both are), without boots on, just to look for Merlin;
Arthur is more distressed in this scene than in the one where Morgana declares war in season five. He’s fretting like a mother hen. Not only he is without breath, which means he was just coming back from his checking around, but he is red in the face and almost yelling in desperation. “Does he expect me to dress myself?!” Because apparently, Arthur literally cannot do anything without Merlin by his side. The way he says, “No sign of him” to Agravaine is so endearing, and he shouldn’t be this adorable. Unfair, Arthur. Really unfair.
Arthur just yells, (and distressingly looks around) in hope that Merlin will come back to him, because he always does. *sounds of my heart breaking into millions of pieces*
And last but not least, Arthur shouts, “Last night!”, which means the actual reason he’s going around searching for Merlin, it’s because he’s worried his world will end without his quirky and clumsy servant by his side (and the love of his life). Merlin is currently out on a quest with Gwaine to look for Gaius, since he has been kidnapped, but the problem is that Arthur doesn’t know this. What he knows is that he has fought with Merlin the day before about Gaius in the council chambers, and believes Merlin is gone for good, this time, and solely for the fight they had. Arthur feels more than guilty that he can’t make it up to his best friend, the love of his life (Agravaine helped Morgana kidnap Gaius, and it explains the ending of the scene, where he understands where Merlin is.) Now Arthur is worried that his last words to Merlin were harsh. He had last seen him when he was done with his duties the night before, and then Merlin disappeared.
No wonder they deleted this scene.