FWIW Akali's total P+Q+E damage at a high level is ~900. That's maybe high, but requires the dance around using the passive and landing the E skillshot + taking it in. Of course she has more Q+P gameplay from there, but I'm just writing out the initial numbers.
By comparison Syndra (the only other champion I spot-checked here) has 700 total damage on her non-ultimate kit. As soon as Syndra hits more than one target with a single ability, though, her total P+Q+W+E damage is higher.
As far as base damages vs ratios, Akali's P and Q are both in the ~325 range for AP to double damage. This is pretty standard across AP champions. E is ~445, which is a bit heavy but not extremely so. Syndra's AP to double is 323, 328, 441 for Q/W/E. Higher means worse AP ratios and thus a tendency to build tank.
So I don't think the tank Akali problem is a function of tuning only. She has similar damage and scaling to a traditional mage. If anything, this feels more to me like she's not safe enough to play her entire combat pattern so she performs better when her build makes it more forgiving. It's very easy for Syndra to land her entire kit perfectly while not at risk and Akali doesn't have that same luxury.