Keeping on the religious theme I've noticed this with the Psalms, even before considering the GPT stuff. I think I grew up taught to be over-dismissive of many types of poetry. I always had an impression that it was mostly just silly space-filling pseduo-deep reused imagery and repetition. School didn't help dissuade me of this.
For me, I think the thing to overcome is to focus on the value of a sense of respect for the author and the work unto itself, rather than just valuing the "understanding" you get from the text (which will always be shaped by preconceptions). A sense of awe (maybe at divine inspiration, maybe at near-divine genius, or maybe just at the sacrifice of time and life-force an ordinary person gave up to create something). For the example of the Psalms, I have noticed that despite finding the language clunky at first, they have a certain way of sticking in your head that prose does not.
A strategy I've been focusing on recently is giving myself permission to reread (and maybe memorize) important/enjoyable works. Reading something twice is basically the opposite of skimming, or a way to counteract skimming. There probably is such a thing as rereading something more than it deserves (I reread Calvin and Hobbes for the zillionth time recently, which I still deeply enjoy but now it's more of a way to relax my mind before bed than a source of insight) but there are certainly works that do deserve it [1].
Anyway, something I've been thinking about a lot as well and I agree that it's fascinating to consider how fundamental is it to the human condition that monks have been struggling with it for millennia. The book recommendation is appreciated.