Guitar lessons in my early twenties:

1-Each week my teacher gave me an arrangement he made of a song. The arrangement was involved with new ideas.
2-I found that I could play the arrangement much better if I memorize it. So, each week I came with a song that I had memorized – I was prepared.
3-I did not play/study the entire song immediately. All music tells a story, so I played the first story, four measures, over and over. I did not go any further, but it was not memorized yet.
4-The next day the four measure was no problem, I played them without looking at the music.

Mark, has a point, there is some kind of hand memory. Not going deep here, just think of how many movements your hand makes during the day – that you give no thought to.
Memorizing a song:

Take as many measures as your mind allows. Play the first two until you are comfortable; then add the next measure --- do not play the song beginning to end. You are teaching the hand memory, it’s like learning a habit. You cannot rush the process.

And yes, learning the theory of chord progressions will simplify the learning. The song “More” has a I VIm IIm V7 chord progression in the beginning. G Em Am D7. You will see this chord progression in many songs, making the task of memorizing an easier task. Most people do not think about any of this, they just forge ahead and play, and enjoy --- and it happens.

John C.