There's quite literally no purpose
I mean, there is. It's to put stakes on what team you'll choose, in hopes that you win. If there wasn't an exclusive reward for picking a side, in our example, let's say that there's no reward at all, than what's the point? Any sense of stake is thrown out, since you're not invested into the Event, there's no real reason to fight when there's no reward past that of tokens that each side receives anyways.
At that point you're fighting for tokens, not the two God Kings.
The stakes of an exclusive icon, force the players involved to actually feel invested in the event, instead of just passively waving their hands about doing missions. There's something on the line, that pushes you to want to win, not just collect all the tokens. If you Win, you get this awesome Icon that shows you're the winner! It's history, from then on, that Icon shows you won.
Giving the losers the same Icon just to make them feel better about losing kills everything above. There's no value in fighting for an Icon, that doesn't mean anything. It becomes trivial.