I agree with what you're saying, but without a proper implementation outside of Windows, the CLR is currently a place where great languages go to die. Mono is functional, but is basically unsupported (for everything but mobile).
No, F# is completely supported by MS. And that's the problem with the alternative languages on the JVM. Decision makers are wary of anything that isn't officially supported by Oracle. There are other problems with languages like Scala and Clojure that have nothing to do with official support, but that's another story.
The mono story is an interesting one. At first people thought it would allow cheap deployments of ASP.NET on Linux servers, but it's really carved out a niche for itself on the linux desktop, in gaming (Unity, Sony's dev kits), and now mobile. What's funny is the JVM is completely irrelevant on mobile, compared to .NET/Mono. Just now Oracle is pulling their heads out of their asses and trying to get the JVM to work on iOS.
You're right that the JVM itself is irrelevant on mobile, but via Android the Java ecosystem still plays a role.
I think you meant "on iOS", not "on mobile". Android has a huge share of the mobile market. And Android is pretty much Java (but maybe you don't consider the Dalvik VM to be a JVM running Java programs).
Also you make it sound like somehow .Net/Mono would be huge on iOS. Just to set things straight: most development on iOS is done in Objective-C.