That's not the full story. I somewhat agree with you on the uke's characterization. He was indeed weak with zero self-esteem, hungry for affection and cheated. But are you purposely ignoring the seme's cold indifference towards the uke? or you really didn't catch it? irrespective of the fact he was doing undercover dangerous work, there was no reason for him to act so distant and dismissive, he was actually indifferent throughout the story with only a couple instances where he gave signs of life. If I had been the uke I would not have cheated, I would have left him. Uke with low self-esteem + insouciant seme = recipe for disaster. These two should not have gotten together, and thus, I do agree that their happy ending was not believable, but not because the uke is a chronic cheater, but because they are a bad combination.
The fact that people justify cheating coming up with thousand excuses is amazing. They were sleeping together, they were lovers. The uke was a weak character with zero self respect, ready to sleep with anyone who gave him a bit of attention or money . Didn't believe in the happy ending or the love between the MC. When someone humps from one bed to another so easy even though they claim to have feelings for their lover, then those people for me can easily cheat again and again.