It certainly would. The reach of .NET was artificially restricted in many respects by making it a component of Windows. Mono provided the ability to just ship the runtime alongside the app, but Mono was also not "enterprise grade"; and of course there were always the missing bits and pieces, especially on the desktop front where such deployment made most sense.
It took a Microsoft that understood open source and non-Windows platforms, and was serious about it, to ultimately get us to the point where .NET Core could be a thing.
Until .NET Core provides support for many of the .NET Framework APIs still lacking from .NET Standard 2.0, many companies won't consider it "enterprise grade".
Examples on our case, WPF, WCF, ODP.NET drivers for ADO.NET.
I think .Net Core will never include WPF.
As far as I know, there are not plans for cross-platform GUI on .Net Core. And WPF is pretty much a dead technology.
Nowadays with dotnet core you can bundle the entire runtime with you binary. The linker is cool, in that it will create a strictly smaller binary, as in "hello world" might be 12mb instead of 50mb. That's cool, but it makes me wonder if .NET would be in a strategically better place today if the linker were present 10 years ago. How many companies didn't choose to write their app in c# simply because a customer might not have the runtime installed?
In any case I'm really impressed with everything Microsoft is doing with dotnet core and hope that I get to use more of it.