I've used boots and shoes on backpacking trips. I roll my ankle a lot less with boots and feel the stickier tread of the boot gives me more traction. Shoes are way better when I'm trying to cover a lot of ground quickly and only have a day pack.
You can talk articles all you want. Really, you show me literature supporting one theory and I'll show you plenty supporting the other. You are fully aware of how that goes. Kind of how no one knows the proper way to eat. But, I digress. I'm talking my personal experience and thoughts from my last 20 years of hiking and backpacking. It's fully a preference based on what has worked best for me in various situations. And, I don't disagree that strengthening your supportive musculature is the best way to avoid injury. 3/4 boots, for me, just add additional protection and are worth the few extra ounces when the trail is rocky and uneven.
All that said, I never made time to do the rim to rim hike (despite living there for nearly ten years). Assuming OP is going Kaibab to Bright Angel, I'd imagine the path is pretty worn and shoes would be fine. You'd know better than I. Just adding my two cents as to when I think boots are worth it.
Life's an endless party, not a punch card.