Enterprises generally don't upgrade anything unless someone convinces them it's necessary. They don't want to follow the bleeding edge of tech, they want to follow the most stable/secure tech with the largest pools of talented workers. Hence the popularity of Java and .NET at the enterprise level.
Picking up .NET core would make a great start to transitioning to a Microsoft-based skill set. That's generally the way those skills are gained - by starting with the latest available to the platform and working backwards as necessary. I started down the path with .NET 4.5 and don't think I've had but a small handful of opportunities to utilize the features in it because most of the servers I work with have .NET 4 as the latest version.