Well, Fire Fists actually have two Synchro monsters, but only the Level 6 is ever worth using (it's the entire reason the 3-axis variant works). I'm guessing since Red Resonator is a Level 6 Synchro off of one Normal Summon, it's used primarily for Horse Prince. 

I've only ever ran Fire Fists as a joke engine for Sacred Beasts, and I've certainly never tried Red Resonator in Fire Fists, but from my rather limited experience, I would say Red Resonator is just an inferior Spirit.