So far I try to classify supports in these categories.
Co-operative supports:
etc.
These supports help the adc get kills. They possess a lot of cc, but that cc is conditional (usually through a predictable, delayed, skillshot) and usually posses some tankiness, and mild damage. Their whole role as a support is to lock down targets to enable their adc to get the kill.
Protective supports:
These supports help the adc by protecting them from others, mostly by healing them. They usually possess at most two forms of cc, one via a skillshot and another on an ultimate. Sure their cc can be used offensively, but it's easier to use defensively. They help their adc by making sure the adc doesn't die.
And then there are
Damage supports:
These supports are designed to do a lot of damage and just let their adc get the kill. They almost always have just one form of cc to justify their position as support.
The problem is that Protective and Co-operative supports are PLANNED supports. Riot released them with the intentions of them being supports and have balanced them accordingly. They cannot do much damage or if they can it is very conditional.
Damage supports on the other hand were designed for solo lane use against other solo laners (usually mid laners). Their kits are designed to fit into the meta of a solo mid lane, where things like farming matter. Sure most damage supports are pretty squishy when focused, but it's way too annoying to try to pin them down when they do not have to worry about cs. Farming is what balances a lot of these champions out because while they may be absolutely terrifying while fed you can punish them while farming. Supports don't do this. This means that every time an adc tries to make a move against a damage support, the support can just....walk back...out of his range and sit there. And the damage support doesn't lose anything, doesn't lose xp, doesn't lose gold, nothing, because their adc is doing it for them.
Now time for me to address your exact comment piece by piece.
"But nope, duo lane has to feel like a solo lane" - Tell me one time where you as an adc were playing against a Blitz, Thresh, Braum, or Soraka and it felt like just a solo lane? I know that a Soraka bot lane won't feel like a solo lane cause you will always be cursing Soraka for healing up their adc.
"And due to how atrocious supports are" - Supports are still in a good spot. Leona has a shit ton of lock down, Braum has good peel, Blitz is great at getting picks and Thresh has a bit of everything with great outplay potential. Soraka lets your adc not die provided they aren't shit, Bard is a fucking balloon, Nami can heal and even peel for your adc.
"The fault starts when you are forcing supports to have 0 presence in game" - A single Leona ult, a good Braum ult, Thresh landing mad life hooks, Soraka heals, these can all make or break a game. Despite how important laning phase is, team fights are what matters the most and a lot of supports have this exact scenario in mind and have a wonderful ability specifically for this situation.
"good base damage and innate utility that allows them to perform adequately despite no reliable income?" - I think your definition of "performing adequately" is misguided. You think that if you don't do a shit ton of damage that you aren't helping your team, which is completely off from the truth! Also I don't understand how a Malz ult and Brand Q +passive counts as "innate utility"? What is more innate then having an ability (or four) strictly dedicated to cc?
"it simply does NOT work" - Worked for 7 seasons. (I know that season 1 might not count cause meta wasn't established etc, SUE ME)
"what's so wrong about changing?" - because with this change the support role loses all uniqueness in it's role. Sure other roles do different types of damage in different ways and travel different paths but they all follow one rule - Kill. The Enemy. That's it. They are all out for getting kills for themselves and their kits are entirely based around it. Playing a support is unique though because it lets you do other things like protecting other players and stonewalling an entire team when they try to gank bot. With damage supports you just poke poke poke until the enemy is low and hope your adc is navigate a kill and if he doesn't fuck em take the kill. It doesn't really matter cause if you get fed that's just as fine.
Your problem is that you are too focused on killing the enemy team and not on protecting your own.
You place little to no faith in your adc to get kills/build properly/do damage so you maim enemies and feed them to your adc like a mother seal nurturing her cub.
And here is the final one. You think that you can't do damage with any of the supports I have mentioned above. Have you build full adc thresh? It's hilarious as hell. Full AP Bard with a Luden's Echo? Stupid as hell but hilarious.