That would be an interesting mode to include. Little rule variation sets, like you say with Overwatch.
I do personally believe that it's worth trying everyone out to some degree, going a mile in their shoes. Even if you don't ultimately end up playing them all that much, it gives you better insight into how they handle and taking that knowledge into a game when you're playing as your preferred type(s).
I've got almost sixty hours on Mercy but everyone else (apart from Sombra, early days) has at least 7 hours on them, too. So I get what that Reaper's trying to do and how he'll move and how to position myself to help out.
It sounds like private matches will be the ones where you can have fun customising the rules and so on and invite people to try them out.
If all else fails, can always talk about it in chat and roll a dice or something to decide on a random counselor!