They can use location information. And gyroscope and accelerometer.
The issue is that apps are diverting attention - otherwise mobile browsers might have implemented push notifications for pages by now. Firefox OS does it, and Safari on desktop has notifications. It's close, but no-one is shouting at the manufacturers to push it over the line.
Flowdock has a great web site that works great on mobile. Their Android app used to be a stinking POS. They then rewrote it to replace the Web View with native to get a different POS. If browsers just supported notifications I could use their web site rather than their app POS.
The issue is that apps are diverting attention - otherwise mobile browsers might have implemented push notifications for pages by now. Firefox OS does it, and Safari on desktop has notifications. It's close, but no-one is shouting at the manufacturers to push it over the line.