WebGL can allow 3D medical, engineering and other productivity visualizations and learning.
WebRTC allows people to mess less with installing 8 different conferencing apps and keeping them up to date.
A built-in PDF viewer allows it to update frequently along with the browser and if properly sandboxes is probably more secure than installing some random PDF viewer setup.exe from somewhere.
Gyroscope, accelerometer and compass APIs allow me to install fewer crappy small ad-packed native apps that I'll use one in a blue moon. Should they be gated by proper permissions? Sure. Why should I trust a random native app with more data than a random website?
I can probably continue with a lot more of these. They boil down to some of:
* If I wouldn't bother installing a native app, then allowing the web to do it enables another use case for me.
* If I don't want to trust a website with a piece of data (gated by permissions), why would I trust a native app?
* The fact that someone wants to use the web just for document browsing doesn't mean there aren't large swaths of users who benefit greatly for using it for many other things.
* There are security holes in the browser. Installing native applications is, in a lot of cases, more dangerous.