Part of the reason why we have different browsers is the variety of features they support. A browser extension inherently is closer to the unique part of browsers that make them different.
What value does this really provide? The times that I've gotten into browser extensions were really working with features that are unique to the given browser.
There's an argument that while rendering engines are huge, monolithic undertakings, the actual browsers wrapped around them are fairly trivial. Assuming they use the same rendering engine under the hood, a relatively lightweight, tightly integrated platform-native browser (i.e. Safari or Gnome Web) might be a better user experience than a cross-platform behemoth like Chrome.
Extension support and depth of extension library have traditionally been the big pain point with switching to a minority browser. Moving extension support into a browser independent standard removes a lot of the selective pressure toward a monoculture.
Well, the APIs that make sense for various browsers can be shared by those browsers. The APIs that are specific won't be.
For example, Chrome doesn't support sidebars. Opera does. So, Opera constructed a sidebar API. Then came along Mozilla, also wanted to have sidebar, and so they adopted Opera's sidebar API, allowing extension authors to easily support Firefox and Opera.
They can't support Chrome, but it's not like people didn't previously already write sidebar extensions when they could only support one browser at a time.
What value does this really provide? The times that I've gotten into browser extensions were really working with features that are unique to the given browser.