The former is a possibility, as we don't have much of a government in the Pokemon nation. The latter I could definitely buy, as Team Rocket is supposed to be a take off of the Yakuza.
I have a different take: I think it speaks of the popularity of Team Rocket, as to why the cops are unable to be take them down in the anime. We all love the Rockets or individual agents (I'm certainly one of them), so it is harder to root for the opposite (the Global or International Police). A big factor is that we don't have the opposite, per se, as we don't know the law enforcement organization in depth or have other officers other than Jenny. They are trying with Looker, and he does appear to be somewhat competent in the job.
(As a sub-sect, we should also consider the Pokemon G-Men, like Lance. Good to know there are additional organizations, with "G-Men" implying a governmental role. At least, in American terms, albeit a tad outdated.)
The rest is what the games focus on: you, the Trainer, taking them down. Not as plausible in real life, surely, but it does sound cool. What sounds better, as a part of ego: "I helped the police in taking down Team Rocket or I took on the whole organization and won"?
Edit: Someone cited B/W 004, with Jenny and the others surrounding the trio. She is improving, and I don't blame her for Flint or Pierce's unexpected arrival, per se. (She should have cordon off the area better, sure, but I don't think that would have stopped Flint, anyway.)