Prior to Chrome, Google actually used to promote Firefox on its own pages instead - which was a major driver of Firefox adoption. Google did it because they had a partnership with Mozilla, and were very much in favor of users switching to a browser that's not Internet Explorer.
Then Google decided they wanted more control over Firefox. Mozilla decided that Google isn't going to get it. This resulted in Chrome.
Firefox was evicted from Google's promotion, and it never quite recovered.
If this is the reason, the remedy doesn't attack the root of the matter. If Chrome were unbundled from Google, what's to stop Google from creating a new Chromium fork - and naming it Cobalt and marketing the hell out of it to achieve the same market share?