Why Memorise?
Why memorise things? Again and again you will see me recommending that you take the time to memorise things. "But that's boring!" you say. Yes, unless you've learned to find it interesting. "But that's hard!" you say. Yes, as is learning a musical instrument. When you learn an instrument, the technique you learn is etched into your memory. When you are sitting and playing, you are either faffing around in the dark, aimlessly, or you are applying those many things you have burned into your memory. A professional guitarist has memorised the hand positions of the many chords they need to play; the professional pianist has memorised the various scales and chords, and has probably memorised a large chunk of their repertoire. Memorisation, in one form or another, is what separates the dedicated musician from everybody else.
Now it must be said that memorisation is not the end-goal. Rather it is as step along the way. Memorisation is how you take a piece and get it all in your head at once. Until it is in your head, you can't really study it, since you are endlessly distracted by the need to re-read bits of paper where it is written down. Just like the martial artist doesn't really start to study their forms, kata, or whatever, until they have the choreography memorised, you don't really begin to study a tune until you know it all off by heart.
And consider a band playing live: they don't have pieces of paper to remind them of the tunes and the lyrics, but rather they have it all memorised. And if you want to improvise, even then you're not making everything up as you go a long, rather you have the mental equivalent of a set of lego bricks that you're exploring rearranging, or tweaking.
Or consider a chess player. They will memorise many lines and variations, so that when studying the game they need only calculate the bits they haven't already memorised. And when they're done calculating, they will hope to remember much of what they figured out along the way, so that they don't have to calculate it all over again.