You'd hit "Next", the screen would push over instantly. But there'd be a loading indicator right in the middle of it until the server returned the necessary data. Asynchronous apps or web sites or web apps will always need to load data from somewhere. PWA doesn't magically make loading go away.
I'm okay with adding offline support, faster loading, and all of that for web apps and sites I use in my browser. None of those features sound bad to me. In the browser.