I really enjoy playing the 1v1 mode whenever it is in the weekly arcade rotation. And I am sure many other people do as well.
My point to make it even more fun would be to re-think the heroes that are playable.
My suggestion: remove heroes like Moira, Baptiste and Symmetra. Add heroes like Reinhardt, and Winston.
My explanation: In the limited 1v1 mode you can chose one out of three random selected heroes that you can play.
Imagine if there are following heroes that you could pick: Moira, Genji and Junkrat. Most of the players would just pick Moira, since she can just keep her distance and throw damage balls at the heroes that can´t heal themselfes. 9/10 times ( in my experience ) Moira gets picked and the match ends up in some boring one-sided fight or a tedious Moira 1v1.
To conclude my suggestion: Heroes that can excessively heal/regenerate themselfes should be removed and Heroes that may actually be FUN to play in the 1v1 mode like Reinhardt should be added.