Well, yeah, you're right, Doom 5 or any triple A game would need to optimise their code extremely high.
You may be doing something that's considered expensive even in 2D or 3D, such as doing too many collision checks per tick (let's say its in the hundreds thousands, your poor little phone CPU will choke on that).
Or maybe your picking logic is too heavy (phones are not databases and you need to minimise reoccurring picking. Even with 80 sprites, if you had several "for each" loops then you quickly multiply the engine needing to re-pick everything all over again).
Or maybe your use of effects (maybe not as you mentioned gpu usage is down).
I'm making random guesses as we have no clue what your game is designed like. How about check the event CPU profiler, see which group of events (if you have used groups) that is the heaviest on the CPU, and then post a screenshot of the events within that group so we can check it out?
Even a typical phone's UI that you use everyday is not updating at 60fps, or even 30fps - it updates the areas of the screen as it is needed, so sometimes it's sitting at 0fps - optimisation is needed, even in games that seem simple!