The CSI Effect.
The “Only cops in the universe” trope is so very far from reality. They get a call that the perp is on the lam somewhere across town, they run out of the building, get in a car, drive miles across a crowded city and somehow manage to be the first ones to get to the perp. This is a dangerous perp, usually with a hostage. This is when every cop wants to be the hero. The main guys would most likely show up an hour after it’s over.
Similarly, they are about to enter a building, they hear gunfire, and they rush in. Rarely do they call for backup, wait for it to arrive, etc. You always call for backup. Always.
Recently, near us, a cop tried to pull over a car that turned out to be stolen. The driver took off, pulled into a parking lot and ran into a store. At least 7 cop cars showed up, we saw it when we were driving by, and more were on their way. I didn’t know that there were that many available patrol cars around here. All for a runner from a stolen car. If shots were fired, cops from every jurisdiction for miles would have come in.
As to the time scale thing in real life. Recently I was called for jury duty, was interviewed for a case and not selected. A bad sexual molestation case. Dragging thru the court system for 3 years.
Really horrible crimes frequently take years to go to trial when contested. (And even then last second plea deals are still made.)
Ummm… there are other kinds?
As for the only cops in the universe thing, here’s another one where I think CSI: Miami was getting really close to comedy. I know this because I’m local but most people would rightly assume… you’re NOT going to have the same cop on South Beach and in the middle of the Everglades, which is maybe 40 miles away.
They executed a man in Texas based on this and bad science. His house burns down with his family in it. Cop thinks dad isn’t acting “right”. PD/DA hire Scientist for hire who makes up shit to say it’s arson. Turns out later, after dad is executed, it’s likely not arson, “hired gun” scientist has a history of making shit up on demand but making it sound good.
To me, looks like the best ‘innocent man executed” case in the last 50 years.
Heck…a few months ago at one of my local bars, we had four cops, a fire rescue vehicle, three fire fighters, and a tow truck show up. And that was for a kitten hiding under the hood of a car.
(yes. And we got it out safely. It ran away. Fast.)
I only watch CSI when I’m visiting my mom, because it’s her favorite show (she’s 95), but a couple viewings were enough to make me wonder who Tim (Sean Murray) had compromising pictures of to get and keep that part, so I looked it up.
Turns out his mom slept with the show’s creator and executive producer. He’s Bellisario’s stepson.
Um, I meant NCIS. Proving how seldom I watch either show.
I think you mean NCIS. 
ETA: Never mind.
To be fair, those scenes are counterbalanced by the ones where the junior cop goes into the building and knocks on the door, the bad guy hops down the convenient fire escape stairs and runs about a mile with all kinds of twists and turns and ducking through alleys, and has pretty much gotten away from junior when he is tripped or tackled by the senior cop, who somehow predicted exactly where to be.
Okay, a bit poorly phrased. But I meant that it was worse than the usual bad sex molestation case based on the charges and the questions asked during the jury interview. I was very grateful I wasn’t picked, would’ve gotten nightmares. Yeah, they found him guilty, sentenced to so many years he’s never getting out.
What’s funny is that if you go back to the really early episodes, they didn’t used to do that. The producers decided that MOVEMENT made for a better scene, so now you’ve got the box stackers and the waitress plate holders and the doctors giving exams while being interviewed by detectives.