That's where the metaphor breaks down (while the intended idea stands perfectly fine), the reason you don't want to waste time making your axe perfectly sharp is that you must learn how to use it first, not because you should just forget about it and go chopping trees.
It has some parallels to most skills, as most times you will only discover your deficiencies by doing it. But it doesn't mean you shouldn't train, it only means that training without ever practicing won't lead you anywhere.
Well, taking a regular break to sharpen your axe, every half hour or after every tree, then you only spend a minute to save five minutes.[1] This is like running tests, or asking questions about what you have done recently to maintain focus on the bigger picture. Or to prevent a commit from getting too big. Or refactoring.
And sharpening a dull axe can take an hour to half a day. [2]
It has some parallels to most skills, as most times you will only discover your deficiencies by doing it. But it doesn't mean you shouldn't train, it only means that training without ever practicing won't lead you anywhere.