Believe it or not, I actually had my first encounter with the "push a button on your phone" to allow login to complete the other day, when I wanted to log in to my Gmail account on a machine that "is not one of my usuals."
This technique is truly convenient, though I still would not want to be having to do that every time I logged in from my own computer.
I can't say that the majority of my clients don't have smartphones, but when you're in a relatively rural area, and senior citizens are a significant part of your client base, many don't. One of my newer clients has his sister pushing him to get a smartphone, which he's been resisting. I have tried to "soften him up" just because of the convenience involved and the fact that the resistance is mostly out of fear of the unknown. I tell anyone that when it comes to smartphones they need only be as complicated as you want them to be. You don't have to use every capability they have, and most of us don't. If you also either clean up your screens yourself, or have someone else do it, such that only your "greatest hits" apps are on display, they become dirt simple to use.