Support Annie gets a Frost Queen, then nearly one shots our Nami immediately afterward.

That's a completely moot point. A champion not having reliable base damage doesn't invalidate the fact that that's what reliable base damage is for. Riven and Annie are different champions. They, like literally every champion in the game, are going to have a different combination of qualities or kit elements.

Annie having high gold indepedent damage is literally half the reason why she can properly function as a support, the role with the lowest income.

Doesn't that ability scale with total AD rather than bonus and allows up to three casts, with the cooldown starting at the first cast rather than the last while proccing her passive with each individual cast?

I mean, telling us that it only has 10 base damage does make it seem weak, but when you apply context you're looking at an ability that can deal up to 198 base damage--(10+56)*3--at level 1. That's more than twice Annie's base damages at level 1. Sure, you have to earn it and land all three, but something something high skillcap I guess? The potential is there to deal a lot more damage, the whole "10 base damage q and gutted scaling" is kind of misleading when it scales with total AD.