ShiroKuro At the same time, I think that for those of us who are "readers," sometimes memorizing could be beneficial just as a way to experience internalizing a piece in a different way.
I do feel that I access "June" in a different way (and it still stuck with me after all these years!) and I immediately related to what my friend said and made the GPS analogy, despite really hating what I was hearing! I literally can't even tell you what note most of my pieces start with and I feel like memorizing will help me to internalize the content of the music better because it will force me to think about what I'm doing, instead of making musical decisions but being pretty "brainless" about the actual notes because I'm still just reading them every time.
Definitely not going to memorize everything but going to try with one piece first and see how it goes.
Also, there's the side benefit of actually being able to play something without music. I feel like everyone should have a few pieces that they're able to play on demand.