Mousetrap Plot Question [Spoilers]

What was the point of showcasing that The Detective is the original "Je Moon-Jae" and was given away.

I feel like that bit added nothing and served as a meaningless coincidence. If it is meant to showcase the Protagonist Je Moon Jae was always a rat since birth. Its pretty weak.

Writer Je Moon Jae figuring out that Protagonist JMJ had a brother who is currently a Detective, and uses Detective JMJ to catch Protagonist JMJ while not knowing that they had a "Uncle" or that the Uncle wasn't blood related anyway.

Feels a bit bullshit to paint Protagonist JMJ to be a "Rat" since birth. Pretty lazy that Writer JMJ can just find that and use it against him. Writer JMJ's main thing that he was able to plan stuff and use a "long con" to beat Protagonist since he had no connections, so throwing this random useless connection has no real value imo.

Added nothing except an unnecessary connection.