The thing is, the whole notion of Zoe having only one damaging ability is a myth: her E alone is capable of dealing 440 (+ 80% AP) damage, which is way above average, and deals a minimum of 220 (+ 40% AP) damage, which is respectable for a mage nuke. Similarly, her W provides an extra 250 (+ 40% AP) damage, even if it's more situational, and her innate is a little over half of Lich Bane's proc. The only reason her Q comes across as her only source of damage is because not even most mage ults come close to 750 (+ 165% AP) damage (even Veigar's ult at maximum damage has a lower base and scaling). In the end, the reason Zoe's Q is so loaded with damage is because she's designed to one-shot opponents, though if Riot really wanted to, she could have her damage spread much more equally across the rest of her kit via pure number changes.
When you look at Zoe, her "real" ult is actually her W, and the rest are just basic abilities, but even so, she really doesn't lack anything in particular compared to other champions: not only does she have a basic ability that surpasses most ults in damage, she also has access to a long-ranged stun that also happens to provide ally utility if she doesn't trigger the bonus damage herself, along with pseudo-mobility that lets her extend her range and buy time. If there's one weakness to her W, it's that the effect she gets isn't reliable, due to its randomness, but that also means she can also gain access to ultra-powerful effects that can completely turn around her lane, or even other players' lanes before anyone even has access to their own ults. Zoe is therefore overloaded in practice, which is part of what makes her frustrating to deal with, but on top of that she is also capable of gaining huge leads based on a factor other than her own skill (i.e. her W RNG), which itself only exacerbates her issues. Given all the tools at her disposal, Zoe doesn't really need to be able to one-shot to be effective, but that has nonetheless been one of her main selling points. This isn't to say that she's seriously overpowered, rather, the problem comes from her design itself being fundamentally unhealthy, imo, so that even when she was still at a 46% win rate in solo queue, she still felt unpleasant to fight against.