I also play a handfull of other competitiv games and guess what I get when I play ranked: A small little "trophy" with the color of my rank in the last season for every season. Nothing else. And there are still a lot of people who play both modes. People who want to have competition play ranked. Those who just want to try things or want to only have fun play unranked.
And maybe I should be more clear on what I mean trophies. I mean litteral trophies. Trophies you can put into your house or titles that specificly tell "Guy who reached rank 1 in season 8". Not mounts and glamours that could also be associated with something else if they weren't already implemented this way into the game.