Pretty much, but the matter is a bit more complicated.
For one, Warriors are the best in the Solo lane because they can solo farm there. That means they are generally ~3 level and one whole item ahead of everyone else. This combined with their base stats which makes them tank-ish, they simply wreck when they start to rotate mid-game.
But if you are the Support, you will be behind in levels and items, which makes them a lot weaker.
The other thing is that most Warriors can very easily clear the lane. Very early this is good because they do not wipe the lane yet but weaken it a lot so the ADC can basically just last hit them. You win lane pressure and your ADC can get ahead. But a few levels in you might clear the wave by yourself as a Warrior because... well, what else there is to do? But that will put your ADC behind as s/he won't be able to stack his items if you kill the minions.
While it is great that you can kill the enemy a few levels in early on, you may steal the lane as a whole. If you are the one getting the kills, your ADC can't get ahead, which is often the aim: feed your own ADC so s/he can destroy everyone.
You may get fed yourself as a Warrior, but it is far from being as good as solo farming in the Solo lane. And also worse than a Guardian Support getting fed. For example Ares fed is a nightmare. He will just kill everyone in the enemy team if he gets a couple of levels and one item ahead. A Warrior can't do that with only that much lead.
To get to the more specific issues, Amaterasu and Bellona has no good reliable hard CC before level 5. Which means they can't really peel for their ADC. After level 5 this dramatically changes as both of them got CC immune high mobily ults that can stun the enemy in AoE.
From the two, Bellona is a much stronger Support candidate tho. She has a Disarm, essentially making the enemy ADC useless for a couple of seconds when a fight breaks out. She is also good at catching Guardians. Guardians are generally slow and a lot of them lack good movement abilities, while Bellona has a short dash that slows her enemies on hit.
To be honest a lot of these boils down to team composition and counter-matchups. For example if you are a Warrior Support, it's best to have a Guardian somewhere else in the team (Solo or Jungle).