Those base damages are late game. Add that all up, and you have about over half someone's HP, while she's on the lower end of Scaling ability Ratios.
Compare to Syndra:
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Q: 230 damage while only needing to hit once (Ahri's needs to hit twice to get 280).
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W: 230 Base damage (While also doing 20% bonus true damage at max Rank) 276 damage
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E: 250 Base
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R: 540 damage with only the 3 Orbs from her normal ult. A single Q pushes that up to 720.
Meanwhile, let's note the diferences. Syndra can do all her abilities from 750+ Range away when level 18 (675 before). Syndra has 75%, 70%, 50%, and 60% (with 20% more per orb to her ult) scalings on all her abilities. Syndra can hit you with a stun from 1100 range away, with a high projectile speed (2500 speed on her E and Orb follow up), and stuns for 2.25 Seconds base.
Ahri has all her scalings only has a 70% on Q (IF you hit both parts), 64% on her W (IF you hit all the bolts), 50% on her E, and 30% per dash on her ult (90% total IF she uses every dash Offensively.). Ahri's highest range ability is her E at 975 range, with Q following up at 880. Her undodgable abilities W-R are 550-600 Respectively. That is incredibly low range for a Mage. Ahri's E speed is 1600, and can be blocked by minions, and Charms you for 2 seconds at max rank, but only 1 second at 1st rank.
But that's late game. Let's look at how much damage they do at level 6.
Ahri does 514 damage total with both hits of Q, W, E, and all three hits from R (which means she used all her dashes offensively)
Syndra does 640 from a Single Q, W, E- and a 4 sphere Ult.
That is a 126 damage difference, and Syndra can do all that from 675 range away, while Ahri had to be within 550 range to confirm all of her damage (not to mention her W has range for each individual flame, so if a minion is within 550 range behind you, you could quite easily lose damage, once the flames start to move).
At level 6, Ahri leaves 316 health left on a 830 health target squishy, while Syndra would leave 190, which puts a huge margin of how much more it would take to kill the person. If we include level 6 ignite damage (170) , Syndra needs a single Auto attack to kill a target, while Ahri would need to land both parts of her Q, without access to her dashes or E, (or 3 basic attacks at .66 Attack Speed)
Not to mention, due to the 1 second static CD on her dashes, her time to kill is lengthened by 2 seconds alone due to needing to hit all 3 of her dashes. Syndra's Time to kill with a Basic 4 sphere combo, can be done at optimal range within those 2 seconds alone. Ahri would need to stick around for either another Q CD, or 1.92 seconds for 3 autos (assuming they're not auto'ing during Combo, but that still adds in Time for an Auto to complete).
So yes, in context of how much effort, Ahri does do less damage than most mages, and has to hit every single aspect of her kit to do so. A missed Syndra Q still contributes 90 damage to her Ult. At level 6, there is no way for Ahri to 100-0 you within the time for Charm to wear off, so you can actually react and fight back while she stays WELL withing any Mage or Assassins range, since she is using every single Dash Offensively.