That Android Webkit thing is an odd internal politics story, though. The Android team was separate from the rest of Google, and the Chrome team always wanted to slip in and replace the Android Webkit browser.
But the Android team wouldn't have it because Chrome was too heavyweight for many years and would have led to a subpar experience.
Android Webkit made a lot of sense up until a year or two ago because it was so simple and fast. But now the mobile hardware and Chrome performance has caught up. Chrome should be the one and only browser from Google that runs on Android. The Android team should simply concede and upgrade Android Webkit by gutting it and turning it into a Chrome launcher, damn the consequences.
Edge, presumably, would be a much different situation than Chrome vs. Android Webkit. That would have Microsoft's full weight behind it and would be integral to their core strategies. God willing, the Edge team won't be competing with the zombie legacy IE maintenance team for resources and mindshare within Microsoft.
The point of my original comment was that a great/competitive evergreen browser from Microsoft without a name would be a scary foe, especially if it ever claimed a majority share of the market.