I know we all laugh about this line because from our perspective Arthur is blind and stupid for not noticing sooner, but I think it actually says something about Arthur’s view on magic.
At this point, he’s not exactly anti-magic the way Uther was (he never really is). He went to the Dolma for help, and acknowledges that the sorcerer helped them win the battle.
However, he is definitely still prejudice against it. But what’s one of the biggest reasons that he doesn’t trust it? Morgana.
Arthur watched someone he considered family go from the caring and kind Morgana he grew up with, to the brutal and cruel person she is now. It’s when she betrays them that he learns about her magic.
As an outsider, all he knows is that Morgana is using magic and betrayed all of them because of it.
In his mind, he is convinced that magic corrupts people. Almost every magic user he’s ever met has either: tried to kill him, tried to kill his father, or tried to seize power at the expense of others. The only true exception is the Dolma, because he blames Dragoon for his father’s death for a long time.
Morgana is the biggest influence on his view of magic; he watched her fall into darkness because of it. He genuinely sees magic as a corruptive force that turns even the nicest people, like Morgana to him, into monsters.
Arthur has had him by his side for years. In his mind, if Merlin had been using magic that whole time, he would’ve been corrupted by it. He can’t comprehend Merlin having magic because he associates it with greed, corruption, and cruelty, and Merlin is the exact opposite.
A lot of fanfics use this concept when writing their own versions of the reveal. To some, it can come across as sappy or leaning too much into the shipping territory, but I wouldn’t be surprised if it was accurate to some extent.
During the first real conversation after the reveal, Arthur asks him a very important question: “Why are you still behaving like a servant?”
What makes this important is the insight into Arthur’s thoughts. He can’t fathom that a person with magic would serve someone, willingly. In his mind, as soon as Merlin “has magic”, he is no longer a servant.
Why would he be? He could topple empires single-handedly. He can create and take life with a few muttered words. He can conjure the elements and manipulate objects with just a thought. Why on earth would a man with that power choose to be a servant?
Arthur thinks that it’s impossible, that no one would choose that. But here Merlin is, taking care of him the same way he always does, even more so given how injured he is. He can’t believe Merlin would choose to serve him rather than pursue power.
I think that’s the biggest reason he says: “I would know”. Arthur thinks he would, because he assumes Merlin would change somehow.