All the PWA stuff Chrome is doing is basically moving in this direction, from the opposite end, really. Instead of building an OS that needs a web based app system, they go in reverse by taking their existing OS and allowing for webapps to be work more like regular apps. This probably will involve more APIs and such.

Building new Web APIs was a core pillar of Firefox OS development, and it applied to desktop Firefox as well. Unfortunately these efforts were bogged down by poor executive leadership and the difficulty of getting any other browser vendor to take new APIs seriously, so the work went pretty slowly.

Gamepad API spec efforts began as part of this, for example. Then another vendor kicked their own inferior spec out the door without talking to anyone and that ended up being the de-facto standard (not the first time). Other APIs like exposing battery status, network connectivity status, and the ability to notify with vibration were in the works, just to name a few I remember.