This is a prevailing thought in the OW community and I think it's heavily flawed for a couple of reasons.
One, no matter how people try to dress it up, being bullied off of damage into the support role is demeaning. Hard supports in fps are, in my opinion, game design in bad faith. On the surface, having a character designed around utility and therefore having low damage output makes sense from a balance perspective. However, the underlying game design intent behind these characters seems to be that they are low skill ceiling classes you can shuffle the noober kaboobers to while the big boys do all the work. For the early Overwatch twitch scene, the most infamous pairing was the Seagull + Shayde combo where he had a mercy health hose attached to his ass 24/7. Not once that I saw in these Seagull streams did he do a reach around and pocket Shayde while she carried. There's a clear power dynamic here that was honestly kind of uncomfortable to watch. Seagull getting bathed in healing juice and looking like a shiny golden god while Shayde screeched and suffered didn't exactly sell anyone on the "joys" of supporting.
The second problem is that despite these healer type of characters being made with weaker players in mind, deathmatch skills are still important to play them well. Positioning, ability use, and decision making are all skills you have to learn to play any arena shooter well. Harbleu a current overwatch pro was a fan favorite TF2 pro back in the day for his wild style on the "roaming soldier" role. At a later point he transitioned to medic and instantly became one of the best medics if not THE best medic in TF2. The ease in which he did this embarrassed a lot of "medic mains" but the reasons why were obvious. The skills to deathmatch properly gave him the raw mechanics to survive, and being aware what a damage dealer needs to do to win gave him the knowledge to facilitate and support what his carries needed. In other words, the best way to learn how to support is to learn how to carry.
The shit hits the fan where these issues intersect. To be a good support you need good mechanics and decision making you learn from playing fps games in a conventional way, meaning shooting people in the first person in a first person shooter. However, these hard supports are completely unattractive to these kinds of people, because of their limited skill ceiling and impact. One of the reasons why you'll see dps players play Ana and to a certain extent zenyatta, but you won't see them hot to trot to play lucio or mercy. Playing lucio for me is complete torture, but at the same time seeing an idiot play lucio and mismanaging everything is even more torture. Lucio's sound barrier and his speed boost and just his cooldown management in general is too important to leave in the hands of a doofus. At the same time at the end of the day he's literally just an aura that wiggles around and hopes to be carried.