[iMiiTH]

A lot of web applications perform really poorly on mobile and apps are made for that nice 'native' feeling. You also don't get push notifications or badges on the home screen. Mobile sites work for news sites and blogs, where you poll for content at your will, but for interactive applications, a mobile application that notifies you of interaction is a must in my opinion.

[weisk]

Have you heard about Progressive Web Apps? They are bringing all those things you mention to the table: push notifications, background sync, offline access, home screen badge...