Edge is not a Chrome reskin, it's a Chromium reskin, and I think that distinction matters a lot here. The point of Chromium is that there is effectively no promotion or marketing in it. I think the fact that Microsoft push pop-ups to get users to move to Edge from Chrome is testament to that.

Now from a technical perspective, more diversity in browser engine might be nice, but this doesn't really contribute to the competition discussion.

(my opinions, not those of my employer)