Stub To me, the argument for memorizing from the start make the most sense.
Oof, unless it's an easy piece, for me there's way too much risk of learning the wrong notes! I think I would want to be at least comfortable playing with the score (maybe not at speed, or still having some technical issues, but at least being quite familiar in my fingers) before adding memorization as an additional step.
Of course we all have different strengths and others who are more aurally focused might find it easier to get away from the score early on?
Stub It would be an interesting experiment to take two similar pieces (you obviously couldn't use the same piece) and memorize one from the very beginning and the other only after you'd 'learned' from the score, and see which approach worked best for you.
I might learn the Chopin "Cello Etude" from the beginning by memory. It's short (!!), I know generally how it's supposed to sound (although not well enough to play the whole thing back in my head) and the only challenging bits are places that I'd probably have to memorize anyway.
I think length, difficulty, and familiarity are major factors for whether I'd consider memorizing a piece at all, and if so, at which stage of learning.