The current major cause of angst in Overwatch are "one-trick" players. These are players who play almost entirely with a single character and refuse to play other characters. The problem is that Overwatch is a game where you can swap characters to better match different situations.
Add to that the fact that some characters are seen as weak, or specialized, and a lot of people become unhappy when another player chooses a character that seems sub-optimal.
The other problem here is that generally, if you play a lot on one character, you become better at that one character than you are at the others. A Torbjorn main can rightfully feel that she plays best on Torbjorn, and would be worse on the character her teammates want her to play.
Of course, no one complains if you one-trick a character who is in demand and who people don't play. Mercy players or tank players come to mind.
Not to mention that if you play in regular team, each teammate often gravitates to the same roles. Dave is the support, Sally is the tank. From an outside point-of-view, this is one-tricking, but the big difference is that everyone on the team is comfortable with it.
So far, Blizzard's stance is that--as long as you try to win--playing one specific character is acceptable. But there are signs that resolve may be cracking. One-tricks are often reported by other players, and can get caught in the automated banning systems.
I wonder what a purely mechanical solution would look like. Imagine that, in competitive, any hero who's playtime this season is more than one standard deviation away from your average playtime per hero is locked out. So your hero pool would be limited at the start of a game, and you'd be forced to play on a wider variety of heroes.
It would make matchmaking more difficult, as you'd now have to account for available heroes when assembling a group. It wouldn't do to make a group where everyone is locked out of the healers (as unlikely as that is).
On the other hand, perhaps your rating in Competitive would be more representative of your ability in the game as a whole, and not just with one hero.