I feel the biggest difference between carrying in Overwatch and carrying in other team shooters I have played is that to carry in OW you need to do more than just perform well as an individual player. In fact, that isn't even the main requirement. To truly carry a game, you need to be aware of what your team needs, what it lacks, and accept the limits of your team's skill level, and consider how to best overcome the enemy team using what you have.
You could be the best Genji in the world, you could be a ultimate hitscan hero when it comes to accuracy, you could be death cancer Mei incarnate, but sometimes that doesn't help your team enough to win because they don't understand how to take advantage of it. If the team understands how to take advantage of that, the conversation wouldn't be about clutching. So instead of thinking in terms of "why can't I use my awesome obviously superior skill playing this character to carry my team to victory by sheer force of will alone", why not think in terms of "we may be losing, this team isn't too great, but if I suggested a few changes, changed into a lead tank or support instead, and if they listen, we can turn this whole thing around". Because that in my experience has a higher than 50% chance of succeeding every time. Of course they have to want to listen. If you are stuck with a team of deadbeats who don't care to work together, you're fucked and you can't do anything, but that's not a game design problem, that's a community problem.
I agree, this is a team game and you definitely should put your team's needs over your own desires of greatness. An uncooperative member that doesn't carry the team's needs is a huge detriment to them.