The menu isn't terribly important at a chain restaurant, but I think it plays a bigger role at nicer local spots. Usually the menus have some nice art in them, something to tie into the theme and feel of the restaurant. It's kind of like album artwork in a way. The food is all that matters, but all the other details can add to a nice experience. I say this as someone who hardly eats out anymore (this was before the pandemic) so when I do, I really want the full dine in experience. Like sitting down and having the waiter hand you a menu. Maybe I'm just old school in that.
Also some take out spots where you can grab a menu and keep for next time you order. While those may stack up in a garbage pile, sometimes it's nice to have one available like we do in my office I share with my coworker. We have the menus of a few of the spots we would regularly grab lunch at. Also a lot of online menus don't list prices either, which is annoying. (I have not seen this for QR code scanning at a restaurant, but usually for chains where the pricing isn't consistent everywhere).