Caitlyn is an awful detective

For a character who was defined in League of Legends by her brilliance as a detective, Arcane Caitlyn is remarkably dumb. Some of her 'highlights':

-Completely unaware that Marcus, her boss in the Enforcers, is working for crime boss Silco. Even being told that Enforcers have been killing Zaunites on Silco's command doesn't make her consider that Marcus might not be trustworthy. Only a completely unexpected intervention from Jinx prevents her and Ekko from ending up dead.

-Falls hook, line, and sinker for Ambessa's false flag attack at the memorial. She seemingly never figures out what happened, instead spending months persecuting Zaun for it.

-Literally sleeps with a Noxian spy for months and doesn't realize anything's amiss until she's at gunpoint.

-Is right there when Vi tells Silco, “What have you done with my sister?" and he replies, “I freed her. Candidly I thought you were the prize of your secondhand family, but Jinx, she’s more than I ever could have imagined.” Less than an hour later, when she sees Vi and Jinx hugging, her response is a shocked, "Your sister is Jinx?"

-Had one key insight in her season one investigation: seeing Jinx's unmistakable graffiti at both the Hexgate airship and the Progress Day bombing and concluding there was a relationship, which is a connection an eight year old could come up with. She incorrectly thought both events were part of a conspiracy by "a single mind behind the undercity's violence" rather than the results of multiple actors with conflicting motives. From that point on, her only contribution is to tag along while Vi solves the case for her.

Conclusion: if you ignore the League of Legends lore and only focus on what happens in Arcane, the only job within the police Caitlyn is qualified for is to fetch coffee for the detectives who actually have working frontal lobes.