Secrecy is of the utmost importance for Haxel.
His plan of shaming Empress Morgana's name will only be beneficial for him if his hands stay clean from the atrocity he committed. Once exposed, he would be branded a traitor and would be hunted down to be captured and punished. Severely punished.
And that would ruin whatever future he was hoping with Empress Morgana.
Naturally, he can't be proven to be the perpetrator and caught.
Rex didn't know for certain what Haxel hoped to achieve from this, or the details of what made him do this, but it was clear that he wanted Empress Morgana. He wanted to somehow strip Empress Morgana of her status by ruining her reputation.
It was an attempt that reeked of desperation.
Just the thought of being held back by someone who can't accept reality—and move on was maddening for Rex. He couldn't believe that Haxel was motivated by something so delusional. Something that did not concern life or death.