The point of having dedicated supports is to expand the number of options your team has. More options means that your team is able to take advantage of more opportunities and react to more obstacles.
Let us consider two scenarios, with two different picks.One is a dedicated support soraka, who builds aura. The other is a AP annie running a kill lane with your adc:
1) The enemy team is doing baron. Firstly, if properly done, without a good ward net, it is hard to detect a baron attempt, especially late game when baron can be done in 10 to 15 seconds. This means that a support Soraka who has ghoststone already has a strong bias in her favor, in comparison to an Annie, whose AP items are useless in map control.
Well fine, you might say, you can just build a ghoststone. But now let us assume that you are not an idiot and built ghoststone, because you recognize the power of wards and are willing to sacrifice personal power for a team advantage. Your team has plat level reflexes collapses on the baron near instantly, who is nowhere near smite range, but their team is well coordinated. Instead of continuing baron, they instead turn on your, with their jungler having taken minimal damages.
In this case, it is likely that they have used some number of resources on the baron (spells, cooldowns, mana), and are unable to operate at 100% efficiency. Given that you are "support ap annie", the greatest contribution you have during that fight is an aoe stun and let's say, 1k aoe damage. But they are not fighting at 100% efficiency anyways, and therefore the aoe stun is negligible as is the aoe damage, if they are, as i said, properly coordinated to mitigate aoe damage.
However, if you are playing soraka, than you can rest easy in the knowledge that everything that you bring to the fight is used at 100% efficiency all of the time. No matter what situation, the 300 hp heal that you gave the tank will always be 300 hp that he can use to further peel or zone a person. The 20 Magic Resist you give to everyone will always be mitigate 20 MR's worth of damage, and a proper silence will always prevent the casting of spells for 2.5 seconds. In other words, a dedicated support would have been better in this situation, not because her power was greater, but her power was used to greater efficiency.
2) Now let us assume that in another game, you are losing and defending against a really annoying nidalee, who isn't quite fed enough to one shot your carries, but does enough damage that if one of the were hit, they would not be able to efficiently fight. The main problem here is that there is nothing an annie can do to mitigate the problems that a nidalee poses to your carries. In other words, her power efficiency at this junction is near to zero. I suppose if she bought a ghost stone, she could ward the area and make is easier for your teammates to dodges the spears.
But an aura soraka on the other hand is able to passively boost the MR of the team, thereby 500 damage to 430. On top of that, soraka heals 270 to the carry. Suddenly that 500 damage is reduced to a much more manageable 160 damage. And this is on top of the warding that Soraka brings to the table. As in the previous case, Soraka is superior to Annie.
The purpose of this post is not to compare the power levels of annie to soraka, but simply to express that soraka's realistic abilities are better than annie's in many common situations.