Paper menus on request seems like the obvious middle ground. Not defaulting to putting menus out reduces the scale of all those problems, while also not alienating customers who for whatever reason don't want to or cannot use the digital menu.
Definitely agreed. I still know a couple of people who don't have smartphones, and even with smartphones you might have a dead battery, a low battery that they don't want to waste on a menu, a busted camera, or for whatever other reason be better off with a piece of paper. Keeping a few real menus handy would be the best way to handle it.