Actually, my guild leader and I combat RPed using stats. We gauged the strength of individuals in combat and the effectiveness of attacks and defense based on your skills.
For example, during our battle the enemy cast Flame Burst. I cast it right back. We decided that, because their rank in the Red Way was higher, their Burst would blow through mine, with greatly lessened damage (they were, like, one rank above me in RW).
I speak only for myself onward when I say that use the descriptions of creatures and people, along with my intelligence to gauge how perceptive my character is, to dictate my character's next actions. I will certainly act tough and threaten some meager swordsman with my magic, but will treat Arch-Mages with caution and respect.
Not to mention judging when I should ICly run away or continue the fight.
You are right that stats aren't necessary to RP. But they make the experience far more immersive and realistic if we set those stats as our character's actual boundaries. Needing to work them up through experience and 'living their life' to become better really reflects actual reality.
I have 'more fun' with stats that way. And I'd prefer if RPers were also considered when you want to 'raise the fun factor'.