Although fight was only keyworded back in Innistrad, the actual gameplay function of two creatures simultaneously dealing damage equal to their power to one another is venerable. But for all its years of existence, and its fairly "obvious" flavor (like a mini-combat without actually creating a new step), it's only appeared on colorless, red, and green cards.
Now, red always gets direct damage and likes conflict, and green has the hunting/hand-to-hand-battle flavor plus could use a means to remove creatures, but other colors could benefit from it as well, as it's an interactive mechanic that utilizes creatures in a non-combat way.
Tumblr user foam-dome proposed another color to put fight in to Mark Rosewater on his blog, asking "What color would fight be tertiary in? My first guess would be white, akin to a gentlemanly duel." Rosewater replied:
Probably white if we wanted a tertiary color in fight.
This doesn't guarantee white fight cards, of course, but an instant that costs W and simply says "Target creature you control fights target attacking creature" is plausible. This avenue of "defensive fight" would definitely be an interesting one for white to explore.