Progressive apps] don’t have to prove their value to users up front. We’re all used to seeing those obnoxious messages when we visit Yelp or some random news source, urging us to install their native apps instead of loading the mobile website. Most of us ignore these nags, because we don’t want to stop what we’re doing just to download an app we’re not even sure about. Progressive Web Apps at least get a chance to ingratiate themselves first.
The End of Mobile Apps (as we know them)
Carine Carmy

I’m incredibly bullish on PWAs in healthcare for many of the reasons you’ve lain out in this piece.

Provide the informational content up front, prove your worth, be rewarded by user who then allows for a push notification, and then live happily ever after.

Trying to outcompete communication, social, and gaming apps for user attention is a development strategy that’s dead on arrival.