Microsoft's ad campaign would be their desktop.

They tried that with edge.

Edge had other problems - most notably, having its own engine that was neither quite IE nor WebKit/Blink nor Gecko, it had to be specifically tested. So there was a chicken and egg problem there - getting web devs to support it was hard because there were no users, but getting users to adopt it was hard because many websites didn't work quite right.

Problem is, at this point it would be hard to convince people to try Edge again.

I think it all comes back to two major issues. First, Microsoft jumped into Edge way too fast when it really wasn't in a position to complete thoroughly enough with Chrome or Firefox. For users interested in the touch interface (I prefer the slightly larger buttons, context menus, etc, even when I'm on keyboard and mouse/trackpad), it was acceptable and had more usable features than the rest, but the actual site rendering, options, and extension support was completely missing, so users went back to what made them comfortable: Chrome.

The second issue is that Microsoft (and it's not just them, here) is terrible about advertising their new features. It's hard to get users to go through walk-throughs and tutorials when they first set up a device, because most users just want to jump to actually using the devices, but I'm a big fan of the 12-15 tab slideshows that Mac devices show right when you first update. It's not thoroughly intrusive (it's pretty similar to Microsoft's "Tips" app), but it's got animations and really shows how useful the features could be.

Microsoft has to get better at showing off new features, and they REALLY need to get better at making extensions available to users. The Microsoft Store just doesn't feel like the best place for Edge Extensions as it is right now.

They may have to rename the browser again.