A few things..
#1. Writing to the WinRT API, which is required for developing for the Windows 8 "Metro" style and Windows 10 "Universal" apps would require a full rewrite from the ground up. Win32 is not supported. They cannot port the existing code, by and large.
#2. Releasing one of these apps would require distribution via the Microsoft App Store. This is essentially identical to the Apple App Store, as far as policy and whatnot.
#3. This would have no impact on the ability to use any streaming services. In fact, it might make the negotiations with 3rd Party streaming services MORE challenging because they'd see it as direct competition for their own apps.
#4. While I agree that mobile is a big part of the future, I disagree strongly if you're suggesting the desktop will go away. It won't. That much is absolutely, painfully clear from Microsoft's results with Windows 8 and their actions with Windows 10.
#5. Of those billions of mobile devices, exactly how many of them are Windows devices? And of those few, how many are high-end devices where the user market is likely to support a premium $50 application?
Of course, #5 is the real killer. JRiver does have a very nice iOS app, and their Android app has been around for a long time. While they are called "remotes" they include streaming functionality, and work extremely well. Robert (the developer of JRemote) has already stated that local playback is on his "to do" list, so I think that is coming in the future.
So, the question is not "Is mobile worth it". The question is: "Is Microsoft's mobile platform worth it?"
That answer is maybe slightly less clear than it was with Windows 8, but it is by no means a slam dunk. I'd, personally, like to see them have a real flagship device that sticks around and is well supported in the market for 18-20 months, and an ecosystem of paid, premium apps from other vendors that are doing well, before I'd invest the massive amount of resources that would be required to build a custom app (or purchase and improve one of the existing ones).
But, you know, I don't work for JRiver. I'm just this guy, you see.