I can't remember the exact chapter but way after that promise was made, he thought to himself that Aria couldn't possibly be still taking seriously something he said in his childhood (maybe that's from when she showed up in the capital before departed on the airship, idk).
So even though he didn't have the mind of a child, he only went along with what he thought she was already talking about to a child (she's shown to be flustered when he talks about marriage because the "partnership" she meant was apparently something else), so he saw no harm in making a promise he wouldn't be expected to keep for life.
As it's been correctly pointed out, he does seem to feel a sting of jealousy when he dreams about her, but the questions he ends up with overwhelm his dense head.
Right now, she's not winning any race, but considering how much the story has leaned into the diplomatic relations between the nations, having a nuke like him would only work for the rest of the world if he marries Aria, marries the princess and she quits being one, or ends up marrying someone from multiple/all nations.
