What problems do people have with supports?

I have to admit right here that I am a support main and that I might be too biased about the matter, hence why I would like some cohesive discussion about what the baseline issue is that (some) people seem to have with the role.

Firstly, my two cents: I noticed a trend which stretches way beyond LoL, in which people somehow reached a consensus that it is good design when supports feel like they are less than a whole champ. That for example playing against a support + any other class should be like playing against 1.7 worth of a champion. In addition to that, there seems to be the idea that supports are not allowed to have a comparable impact as any other role.

I always assumed that that had something to do with the dominance of dmg roles and how anti-fun it is for them to see their (hard) work negated by (point&click) supports. That point loses some credibility with the adc hunt that it is going on right now. However, I feel like it is exactly that hunt which warped the support role into a weird and undeserved position.

This is especially aggravating since the role covers a wide roster of champions with a lot variety. So throwing the same argument out there about insurmountable heals and shields feels strange at best.

This whole post is to my shame full of speculation and so called shower thoughts (not as cohesive as I would like). So I would highly appreciate some insights into the games mechanics and general gameplay which support (or don't support) the position the support role is currently in.