Enterprise applications are a different beast, especially if they are report heavy. Having said that HTML5 does have offline storage API albeit with a 5MB limit though support for it is up to the browser.
HTML5 also has Notifications API[1] which can be leveraged for push notifications on mobile devices.
I do not disagree that there are many use cases for using Apps especially in the Enterprise space but there are far too many consumer apps than enterprise ones so maybe I should change that statement to "a majority of native consumer apps" :)
[1]https://mobiforge.com/design-development/web-push-notificati...