Is it a good idea? Like they arrest some transmigrator for war crimes. The summoners for kidnapping. And even arrest them for the heinous crime of tax evasion.
I mean yeah? Then again it is not a common story idea in wns - you are much more likely to find such stories in older anime and games
ooohh how about they have to pay tax every time they do interdimensional travel and doing so without license something like normal airport security but you are doing interdimensional travel
It sounds interesting, but how would they do it?? Do they have some sort of system monitoring the space between dimensions?? Is their hq located in that “space”?? How do they recruit people?? Who pays them/fund them and why?? Not all of these have to be answer, in fact, you could ignore all of those questions. But they are something you can consider.
It's not a story idea. Your story idea should be something like > A detective for the interdimensional police department is working a case and stumbles onto a bigger case that puts his/her life in danger. The villain turns out to be his/her boss! The interdimensional police department would be part of the background. It's flavoring for your story, not the actual story.
Here's something similar, but agreed interdimensional cops would be way more interesting. "The One", parallel universe travel to consolidate power "Time Cop", time travel to prevent people from changing history "Rick & Morty", riff on Time Cop episode