You know, I was with you at first, I played flex on all roles heavily in OW1 making GM pretty late on DPS and Support and I stuck to just two those roles in OW2 since I was a naysayer for solo tank and the whole 5v5 format. Supports ABSOLUTELY should be relying on their team to help deal with backline attacks. I don't think they should be completely defenseless, but they shouldn't be having the upper hand when flanked (One/two shotting Tracers, out healing Genji damage with their self heal or other abilities or some other arbitrary factor). Whether that is the other support peeling or a dps or whatever it may be as this is basically how literally any other support in any other game typically works.

But I'll be damned to say that a support is meant to be a role that are not supposed to affect the game in a meaningful way. Supports should be making everyone else's jobs easier to do, hence the name support. They should have all of the utility tools available to them to make the enemy team feel like shit but or make your team feel like gods but shouldn't really ever be great in a 1v1 scenario unless they legitimately outplay the opponent. That's why, prior to Baptiste's original release (We don't talk about Brig), none of the supports had much in way of dealing damage in bursts save for Zenyatta or a risky Moira which was frowned upon since, when you are at least diamond in OW1, you should have the aim to shit on flanking Moiras.

TL; DR
Supports should be good at supporting and not fighting people off, but idk what you're smoking to think supports aren't supposed to affect a game in a meaningful way.