I don't disagree at all about what you say about fighting games, since they even NEED to have constant solid frame rate to even work properly online as well.
It changes a lot actually, you just seem to not be used to it.
It's not only about that.
I'll give you an easy example:
You enter a hall as soon as an enemy was entering a room from the same hall. If you are playing at 30fps and you are unlucky, maybe you couldn't see that person entering the room, even if the only thing you could see was his foot left, which you could see if you had more fps.
In short, having less FPS means the game cuts frames so you objectively see less of what's happening. Most people don't realize about it since, I admit, one has to be kinda obsessed to it to easily notice the change.
Having less fps (say 30 compared to 60) feels more cinematic because you feel less owner of what's happening. You see more than what actually is because it's just your subconscious trying to replace the empty places, so explosions and such seem to be a lot bigger and messy than what they are at 60fps or more, because at 60+ you are able to see it all and it's not as impressive as it seems at 30, but in truth, you also see more realistically that way and are more aware of what you are seeing all the time.
Pretty basic concept tbh