If you forget a line in the middle of your scene, you want to have the page right there. And you must get used to glancing down without losing the connection to the reader or your story. Now you are very likely going to think, "I spent all that time memorizing my lines, I am off-book. I have to be off-book." But why put that pressure on yourself? Having memorized every word does not guarantee a great experience for anyone. Nobody was ever cast because they got all the words perfect. It's crazy to put your main focus on knowing every word and then wish you had the page in hand. Having a map to refer to offers support so why not support yourself? Especially when you're showing up with strong choices, comfortable in your own skin, with the confidence of knowing who you are and what you want in the scene.Plus doing that kind of prep work ensures you know your words far better. Holding the script reminds us all what this is. While you want to come into the room and do your work at the highest level, having your pages solidifies that we are in the early stages of our collaboration, that this is your take on it, that we are all in discovery, and that you're available to direction. It also allows us to relax,knowing you have your pages if you need them. And it's great to have something to hold; pages are a prop of sorts.
But here is what's most important. Focusing on the "should I or "shouldn't I" regarding a script in hand is focusing on that which undermines your power and talent. It undermines your confidence in yourself. If you want them (the studio, the network, the producers) to put millions of dollars and their careers on your shoulders, you have to show up in command, rock solid ,knowing exactly who you are and what you want. Your pages are just an extension of you. You hold them as needed,you use them if you have to. You know what you're doing, you're deep in the work with your own clear, strong point of view. You're in the driver's seat.
When you're deep in the work, when your confidence comes from how much you trust your instincts and your preparation ,then and only then are the pages secondary. Doing that kind of bold work is what you strive for, not focusing on whether or not to hold the page. Focus on what's truly important, then they won't even see the pages. They will be so engaged in you and your story, that they won't notice anything else.