This is pure speculation. Maybe they're doing something shady with edge that would get them in more trouble(or found out) if they put in enterprise systems, but they see the regular consumer market as easy targets who can't defend themselves. That might explain why they're pushing edge so hard.
IoT Enterprise and LTSB are for embedded systems, they lack many of desktop applications and features (like Cortana) found in "regular" Windows. Windows 10 Enterprise is the desktop version, it has everything in Pro, and then some. There's nothing "shady" about Edge.
To be honest, I think that it hurts Microsoft more than anyone else. It means that corporate desktops using VDI, and presumably Web kiosks, now have to use a third-party browser. In some cases, Edge literally can't be an organization-wide standard, and Internet Explorer is now frozen, so people will have to move away from it over time. For example, every VDI Windows desktop provided by AWS Workspaces is actually pre-loaded with Firefox.