Most commercial JVMs also have native compilers for Java, and there are a few projects to run JVMs directly on top of hypervisors without OS in the middle.
I'm referring to the open Hotspot which almost everyone uses, not some specialized JVM products which are closed-source. You do bring up an interesting point though.
As for the type of hypervisors you're referring to, those things are effectively half-baked operating systems. That's why something like KVM is better -- you're not pretending to be a non-OS while slowly reinventing a wheel that the *nixes have and always will do better.
I think we're beginning to wander massively afield though! :)
Some of those are actually LLVM frontends.