First of all I have to say that this obviously doesn't apply to all cases or all toxic players.
I've seen a lot of YouTubers complaining about private profiles and not being able to see what other people play. I want to make the case that they are actually a net positive to the game and an important part of the most recent suite of social features that have drastically reduced in-game toxicity.
Yes, I agree that in a few situations it is an inconvenience to not be able to see what other people on your team play. I'm not so sure that has more impact on whether or not you enjoy a game than what it does to serve the goal of reducing toxicity. It's not just good players that now can't see your profile, but also toxic players who research their teammates in an attempt to formulate the nastiest possible insult.
I'd support the suggestion floating around to make the default setting public, but I know that personally the first chance I got I would set mine to private, so I can play Quick Play games without getting abused for my rank, the heroes I play or whatever else someone decides to take exception with.
I think that the community, or at least the worst elements of it, has proven that it can't be trusted with that information. It's a shame, but it's evident that incentive to be nice and less toxic ammunition has drastically improved peoples' behaviour in-game. I'm now concerned that if Blizzard folds to demands to revert this, that the aspect of "Overwatch Manager 2018" will return and games will be less playing, more sitting in the spawn room ranting at teammates for playing a hero someone doesn't like.
I guess I should also add that this is coming from someone who has recently opted to stop playing Competitive mode and only play Quick Play, because the quality of games and level of toxicity in Competitive season 10 were a definite nadir for the game. Either way, I'd rather play, have fun and lose a game with nice people (forced or otherwise) than spend half an hour in a free-for-all barrage of insults.