This is a great perspective that I hadn’t considered before.
My previous experience, years ago in high school, was absolutely the former. I think it makes tons of sense to try playing a wide variety of pieces at my skill level.
I am just beginning to learn piano and when I told my teacher that I was memorizing the pieces I was supposed to be reading, he told me to simply play each piece once, mistakes and all, and continue on to the next - specifically to practice playing a piece on first sight.