Memorisation will set you free. Free to play, to explore, to create. In acting one of the first actions an actor takes is to “get off the book”. Why? For the very reasons stated above. Therefore, examining boards require memorisation: to set you free. Free to discover and play with the composer’s intentions. This is difficult to do if you have your head buried in a score.
The following video of Dr. Mortensen explores various methods of memorisation.
Practice room memorisation and it's dangers.
He explores in depth these topics.
You've got to learn your instrument. Then, you practice, practice, practice. And then, when you finally get up there on the bandstand, forget all that and just wail.
I'm a professional pianist and music educator in West Toronto Ontario. I'm also a devoted student and teacher of the drums.