I think you can have combat focused stories as long as your combat mechanics are lightweight and fast.

When I switched out my Shadowrun game to The Sprawl, and then eventually a homebrew, I actually got less afraid of letting combat happen because I knew it wouldn’t eat up ninety percent of the session. By volume of time spent, combat became much less of each session, and yet conversely combat could happen at any time and every scene could feel like a fight might break out because there was no sigh “Roll for initiative…”

With fast, lightweight combat mechanics (especially ones that do not have an initiative system) you get to weave violence into the substance of your story constantly, without the system taking place of the storytelling.

That’s not to say that less combat focused games are a bad thing. The other big change I found was that it was also much easier to run sessions where no fighting occurred, because I didn’t have to figure out how to fill the several hours that should have been taken up by a fight, and the players never felt like there was a difference between fighting and talking and everything else. It all just became part of the broader texture of the story, so a session with no fighting didn’t feel weird or out of place.