O I don't know if that's 100% true. Granted, I'm with you in that things described as Martian-this, Martian-that, are quite silly.
Part of what I'd like to introduce for J'onn is a grand mystery. He's a detective as John Jones, and I'd call his equivalent on Ma'aleca'andra an "Inquistor". I'd like to have J'onn be from a Mars that's reaching the height of their civilization during Earth's Cretaceous Period, 80 million years ago. That's a significant amount of time for Mars to be a very different place than it is today.
So let's assume J'onn knows a little bit about the universe, but what he does know is extremely outdated information. And while he has suspicions, he doesn't know what happened to Mars. It's a crime that haunts him, and drives him to 1) work toward strengthening Earth against an alien invasion and those agents who might conspire with extraterrestrial invaders, and 2) explore the DCUniverse to learn more about what happened to his people and what happened in the millennia following its destruction.
The above sets up a situation where the known DCUniverse is a film noir crime story, dressed up as an ages-long space opera. Our solar system is the chalk outline of a planet's murder. We get to learn about the DCUniverse through the eyes of a
Rip Van Sherlock, and discover along the way that the civilization that once covered Mars has left a blood trail throughout the known universe. Adding to that: Earth is potentially at risk, should the perpetrators ever return to the scene of the crime. You get John as a detective, you get J'onn as the director of the DEO, you get J'onn as a motivator for the creation of the Justice League, and you get a reason why he might leave the planet from time to time: he's following up on a tip.
It also makes the discovery of Miss Martian an amazing, heart-breaking connection to a world thought long expired.