This is a completely ridiculous statement, because you assume that an axe is just an axe.
There's a huge difference between a woodsman's axe, a battle axe, and an executioner's axe. They have different weights, different balances, and even different edge types. Yes, any one of them COULD be used for the other in a pinch, but it's not ideal.
Point is, humans have been designing weapons specifically to kill titans for seemingly centuries, and for whatever reason, they've determined that overgrown box cutters, and not axes, are the best way to do it.
That, or they simply weren't aware of what they were yet. Since transformation requires a very specific set of circumstances.