I think a piece can also be "learned" just reading it.
THis means, that if I would play it over and over the actual art of piano playing would become in danger, just because there is no change, just repetition. I recall my private teacher.
At least, we did a Bach, an etude, and a performance piece, meaning Beethoven sonata, Schubert,... So, we let things rest for a while and come back.
But, it would be worth going into the actual learning by reading. Richter learned a piece on the train, and performed it once he arrived.
So, the analytical way is something to consider. But as I lack harmony training, I think it's harder, but worth a try.
I'm working on early Schubert klavierstucke, and Schubert often modulates from major to minor. This means, double sharps (how do you call that I don't know the term), flats where the key of the piece is major. So, hard to read, with all the modulations. This could be learned upfront analyzing the piece.
I have to try it. I think it sharpens the ears in the mind to.