I’ve been learning piano for over a year gradually learning more and more pieces like that, and I’m starting to notice a limit to memory. The basic melody is easy to remember as you point out, but piano music often has multiple things going on at once, and it gets harder to keep track of all that in your head.

The best piano players in the world play by memory whole concerts evenings with incredible complex and hard to remember music like JS Bach. They play hundreds such of gigs a year reliable with a very big repertoire.

And of course, very often not only their own parts but to varying extents, those of their fellow musicians if they're not playing a solo composition.

I think, maybe to the OPs point, that would require you to either 1) remember the tune perfectly to recreate it, 2) or to have a recording that you can continually reference. #1 is still unreliable and sheet music was created when #2 was unavailable.

I'm personally envious of those who can play by ear but have found reading music to be easier to learn by comparison and more precise.

I learn by sheet music and ear. Ear is by far more precise because of the severe limitation of musical notation. As Mahler said: The essence of music is not in the notation.

I see your point and I think you’re right. Notation is more limited. To clarify, notation is more precise for me due to my limited ability to differentiate well enough by ear.