Using the mobile web as a constraint to think about web design is growing in popularity. I see it in my own efforts and the efforts of our portfolio companies. When users spend more time accessing your service over a mobile device, they are going to get used to that UI/UX. When you ask them to navigate a substantially busier and more complex UI/UX when they log onto the web, you are likely to keep them on the mobile app and off the web app.
I'm starting to think a unifying vision for all apps should start with the mobile app, not the web app. And so it may also be mobile first web second in designing web apps these days.
