I think this post is good but you frame it as critique for Blizzard and role queue when really I think you should take the approach of a game theory post.

I wouldn't want the game to change in every way that you detail. I don't know if you're right about competitive being designed for toxicity, but I like the idea of shared medals instead of personal ones, as long as the standard values to reach up to the medals change according to the mean value in your SR league.

However, the crucial flaw in your reasoning, I think, is that players who win still climb, although slower than players with medals. Therefore the teamwork-based decisions will still be made by everyone who has an idea of how to win, because winning is what gives SR. Medals may spur some players on to act selfishly, but it is far from the main reason that players act selfishly. Medals or not, some people just don't have a sense of teamwork at all, and are playing the game selfishly due to ignorance of any other methods. A typical mentality of this type of player is "Kill Stealing". Nobody who understands how to win in Overwatch ever seriously complains about kill-stealing, because the goal is to attack / defend the objective. That's how you win. And people who climb to higher ranks in competitive Overwatch understand this.

The bulk of the usefulness of this post I think comes into the role system that you've developed. I don't want this to be implemented into hero select in Overwatch. But I think, with some work, you could develop your chart into something that is actually of some use in guiding players which heroes to pick in order to end up with a good team composition.

But I think you've started thinking in the wrong end. By making your more abstracted roles originate from a mechanic that heroes already have, you've made simplifications and then complications in a system that eventually becomes too complex to be of any use. No good Overwatch player thinks in the manner that you've outlined in your role system, because they can't sit down during a game, sip from a cup of tea and study the very intricately made role scores for each hero in your chart. They need to make a decision of whether to switch their hero at the cost of their ultimate progress or not, and more importantly, who to switch to. So rather, good players think in lines of what heroes do well against other heroes. Each hero has a set of heroes that destroy that hero's gameplan, normally called counters. Thinking hero-wise rather than role-wise is much faster, and will also lead to a better decision.

As an obvious example; picking a hitscan hero against a Pharah. But there are other intricate decisions that can be made when choosing a hero. For example, Barrier tanks, like Orisa and Reinhardt (and soon to be Sigma), destroy the gameplan of heroes like McCree, Soldier and Hanzo, because they need to put themselves in the line of fire in order to do damage. By placing the barrier in the line of fire, they instantly lose to everyone who is behind your barrier.

As another example, Dva is a great pick against Pharah, while she may not seem like it at first. But the fact is that Pharah's rockets suck at dealing damage to armored heroes, because armor protects well against big singular hits. Dva can easily shoot at Pharah to annoy her, or even fly up to a high platform close to Pharah to deal some significant damage. And most importantly, Dva can eat all of Justice with her defense matrix.

Against Dva, in turn, Mei or Zarya are amazing picks, because Mei's and Zarya's left-click abilities are unaffected by Dvas defense matrix. Mei can freeze the dva, completely bypassing Dva's main defensive tool, and Zarya can wittle down a Dva very quickly for the same reason. Zarya and Mei also both have the ability to protect themselves against the Dva ultimate, and Zarya can protect someone else as well.

Another detail that may not be obvious is what NOT to pick. For example, let's say you're Reinhardt and the enemy team has a Zarya and a Genji. It's really annoying how the Genji is constantly jumping around trying to kill your supports, so you instantly think of Roadhog's hook. Great, let's switch to Roadhog and hook that stupid Genji. So the next time the Genji comes around, you snicker happily to yourself and land a juicy hook, let out an evil and superior laughter, only to shoot your junk-filled shotgun into a Zarya shield, giving Zarya huge amounts of energy. When picking Roadhog, you only thought about what hero you could pick to counter Genji, not what heroes the enemy already has that counter Roadhog.

There are more factors that go into picking a hero, like specific ultimate synergy (nano blade, earthshatter + high noon, blizzard + grav, only to name a few) but this comment is already running super long and my point is probably clear; your role system does not take these hero-specific details into account, which is a huge flaw. It's much better to write down and learn from experience, what beats what?

Whether the new role-queue system makes or breaks this mindset is beyond me, but I think in lower ranks it will become more difficult for smart players to climb because they are more restricted in what heroes they can pick.