One reason it's so good is it doesn't rely on twists like other mystery type stories. You always see the crime happening in the first few minutes with full confirmation on who did it. So the audience has all the information already, you're watching Columbo put it together and trap the criminal. So you're not figuring out the mystery alongside Columbo, rather, it's like he's breaking down the whole story for you. It's really formulaic, but it's usually fun and varied.

He's also just not a normal cop. He's a weird small man who's annoying and talks about eating chili. He's usually only shown solving crimes committed by completely vile smug assholes. My favorite episode is the one where Leonard Nimoy plays a surgeon who wants to steal his colleague's research out of a lust for fame. So Doctor Nimoy comes up with a plan to purposefully botch his colleague's heart surgery, but a nurse finds evidence of the plan, so Doctor Nimoy kills her with a tire iron and makes it look like a random heroin addict killed her. I love this episode because multiple times Columbo drops the dopey goofy detective thing and lapses into anger. He tells the surgeon just how despicable the whole thing is. I guess that's the good thing about Columbo, is that he has the outer vibe of an everyman. He's just some gremlin man from New York who talks funny and has an invisible wife. But at his core he has a sense of justice and what he despises most are abuses of power.

He's not a real cop is what's good about it. He's a heroic character who doesn't have a real life analogue, so he's a cop out of writing convenience. He's more like a whimsical spirit of justice than an LAPD pig.

It's definitely not just that the crooks are rich. Not that I watch a ton of cop shows, but I've seen many episodes of shows like Law and Order where rich people get taken down. The writers are smart enough to know that's what people want to see, and it's part of how copaganda works.

I think the thing that makes Columbo feel so different is that every episode is like an intellectual duel between Columbo and the murderer, and the tone is usually pretty light and sometimes comedic. Then there's Columbo himself; I know he's technically a cop but he feels more like he's from the tradition of Holmes or Poirot. He's a detective because he's an eccentric. And the fact that he's seemingly given such a wide berth by the other police makes him feel independent, like Poirot or Holmes, and not part of the police power structure.

he goes after rich people who think they are untouchable, he doesn't use violence or aggression (except in the first tv movie), he hates guns and doesn't carry

I think it's in large part because Columbo isn't really trying to portray a "real" police officer, but instead a pleasant fantasy. Shows that try to emulate what's real are also usually fantasies, but they don't portray it like that, instead trying to portray abuses as "good" or "necessary", and dealing with serious topics only on the surface level.

Columbo doesn't wear the uniform most cops do, he doesn't really do "beat cop" type activities, he's the kind of cop most people will never interact with. He also has a very distinct and recognizable persona and style. If you take a look at the worse cop shows, the police officers tend to be very similar, less distinct.

Also, I think that "The Wire" is pretty good, despite being a cop show. It tries to be real, but it does a much better job than most cop shows. It's not all black and white, and doesn't hide a lot of the issues the way other shows do.

Probably all those factors, Columbo would still work as a character (or would be even improved), if he’s was a police officer/people’s militia under dictatorship of the proletariat.

Part of it is that Columbo was made before Dick Wolf barged onto the scene feeling like cops didn't get sucked off enough by ~~state propaganda~~ private individuals with common interests, influence and links to the ruling regime. He also felt the need to vilify public defenders.
Brain worms were still ever present back when columbo was made, so it could still have been awful (look at one of the first cop shows: Dragnet if you doubt me). But back then there were room for more "common" people in the entertainment industry and it was made right between the red scare and the Reagan red scare, so you could get away with being a little leftists as a treat.
That's my theory anyway

Because Columbo would have solved the Kira case

My favorite thing about the show is that while often times maybe you're not gonna catch everything columbo catches, and some stuff can be contrived, the show is still begging you to pay attention. If you were impressionable and going to model whatever came on your TV, being observant and thoughtful would be the outcome for watching this. Columbo always notices details that are amiss - the idea that if something like a murder has taken place, but has been staged to seem accidental or otherwise non-criminal, there are tells. there are signs. there are disturbances. inconsistencies between people, alibies, and the truth of an event - and i think i love that. It's a good moral to try and impart, but i think it might be lost on decades of boomers, gen xers, millenials, and zoomers memeing too hard, but i also think it's right there to pick up on if you're willing

Columbo is a cop but Columbo isn't a cop show. It's a twist on the classico murder mystery but otherwise falls into the same Holmesian lineage of poirot and Jessica Fletcher. It's a vibe thing

Probably helps that Peter Falk is like a real big-screen cinema actor and an absolutely fantastic one at that and that a lot of the early episodes are also directed by actual movie directors and not TV directors.

besides him going after rich people, he also goes after a police commissioner or something like that, and a CIA agent I think.

columbo clearly has some preternatural sense but through the hard work of peter falk we end up with a little guy who we root for no matter what, AS IF HE NEEDED IT..

if you're gonna watch poirot and columbo, anybody out there, watch poirot first. it's not an enviable comparison!!!

We need a modernized anime Columbo

I gotta watch columbo

The Columbo Cooking Stream

https://youtu.be/J9b5Vp0SE3Q

It aired before the American TV industry got in bed with the FBI to demonize unions by portraying union lawyers as a pack of murderous criminals.