Ilan is doing some incredible stuff with alternative materials. I envy him for that! In regards to the type of models he's creating, I'd say he's actually concentrated in tessellations. Know what I mean? He puts his tessellations to different uses through the unconventional materials he is using, but they aren't practical models per se.
There are some business card holder designs which are supposed to be practical. I have designed one myself (https://flic.kr/p/NE3Cu7) and I folded one designed by Shuzo Fujimoto at the last German convention.
Your question certainly piqued my interest from both an artistic and functional capacity--though I recognize how broad an overlap these elements have days--on how amazingly practical Origami has been in addressing thorny and difficult "real word" applications.
I, too, am fascinated with the functional, utilitarian components of Origami. So much so, that I want to integrate it as an important (and central) feature of something I am trying to invent. I've been folding for a few decades, and watched practitioners across origami landscape help it enter its second (third?) Renaissance, so I recognize the astounding potential inherent in what we collectively love to do.
Unfortunately, my project requires a some input from people with a solid mathematical as well as materials science background. As my project is something I would prefer not to broadcast across the ether--at least not the overarching goal--its been difficult to solicit help online. (Though I'm sure there's a way.) Trying to tap local academicians has been even more daunting. But I digress. sorry.
Kudos for your candor in expressing your interest in exploring the practicality--however you wish to define it--of Origami. I feel the same gratification in seeing how expansive and unexpected the applications for this beautiful craft form have become!