There can be a big controversy about using a music stand while performing on stage, I don’t really want to get into that but rather what advantages there are to memorizing pieces of music.
I would say memorizing will improve your skill level. The only way to memorize a piece of music is through repetition and the more you play a piece of music the better you will get at it. This will also help to build your technique.
Having your music memorized will also help with your confidence. If you are relying on a piece of music in front of you it’s easy to get lost due to nerves or distractions while you are playing. Distractions can range from a loud audience member to an equipment malfunction and everything in between. I can’t tell you how many times an audience member has come up to me during a song to request another song. If I am not completely confident in the piece I could get lost very easily. Another advantage is you have everything memorized you can interact with your audience better and have eye contact.
There is an old saying. How do you eat an Elephant? One bite at a time! This applies to memorizing music. I memorize by taking a small portion and play it while reading a few times then I turn the music over and try it I do this until I can complete that passage with no Problem. Then I work on the next package and put them together. Before you know you have the piece committed to memory and you will be much more confidant in that piece of music.