Now, somebody is going to argue that memorizing isn't reading. But I'm thinking of reading in the very broad sense -- the input part of the input-process-output learning mechanism. Listening falls into that category, too. Memorizing is just a more focused, intense form of input into the brain, so yeah, it's "reading".
I memorize. For some reason, God just designed me so that memorization comes easy for me and is fulfilling. When Leslie was a newborn, I started memorizing the beatitudes, and then continued on with the rest of the Sermon on the Mount. And then the book of James. And then Galatians. And then First John. I'm not bragging, and please don't be impressed. Like I said, I'm just made this way. (When I was seven, I memorized the Gettysburg Address, just for fun. Little freakish me.)
I only bring this up because I learned with all that scripture memory the value of having meaningful words stored away in your heart. To remember the order of ideas, I had to look for a flow of thought between the different sections, which gave me a lot of insight into the meaning of the passage. To remember unusual words and wording, I had to consider why the writer chose those words, which again gave me food for thought. I found verses and phrases coming to my mind automatically when I was in life situations that called for them. Basically, the scripture became a part of me, a part of my thinking, a part of my worldview.
This is why I was very conscientious about the scripts I wrote for the homeschool drama programs this year. These kids were memorizing this stuff. Some of those words will be with them for the rest of their lives. May as well make those words count.
Many classical education homeschool resources recommend that students memorize literary passages on a regular basis. Kids used to do this all the time in school. Read Laura Ingalls Wilder's books and you hear about them having to recite poems, essays, speeches, even entire history texts. Reciting out loud adds even more value to the practice. To recite expressively, you have to really think about the meaning of the words, the emotion behind the passage.
You own a piece of literature when you memorize it. I know this isn't for everybody, but don't knock it until you try it. Try more than just a Bible verse or a one-sentence quotation. Challenge yourself with a passage of significant length, one that has a lot of meaning for you. Add a sentence or a phrase every day. Run through it in your mind while you're filling up the gas tank, unloading the dishwasher, whatever. See if you aren't ultimately changed by the power of the words.