I wish I had this issue with being able to free pick a healer, usually someone ends up picking Mercy before I can, and so far I've been sticking to Mercy/Zenyatta for my comp matches (Usually Zenyatta when we have a Winston).
I think I ended up playing Lucio once, and I still just can't seem to enjoy him, more because I find it annoying to keep track of people's health bars when you have to actually look around to make sure they're in your circle of healing.
Also, the last time I did play Lucio, I had a Widowmaker standing across the map basically spamming how they need healing and then insulting me for not healing them.
As the only healer.
Yeah, totally gonna ditch the team to heal the sole Widowmaker.
Honestly, I feel like if you don't get the point immediately on KotH as Symmetra, you should swap off. Her turrets are borderline useless at that point then as long as the other team is smart and doesn't overextend.