This question is likely to be closed as opinion based. However, with that in mind, here's my opinion:
Your question doesn't really make sense. It conflates the purpose of an operating system and a runtime. Operating systems are virtualised, which allows multiple operating systems to believe that they are running on a dedicated processor, whereas in fact there's a hypervisor running at a different level below.
The JVM doesn't deal with hypervisors, since it doesn't run on the processor directly; it runs on the OS. You can run applications side-by-side in an OS without any problem, and they'll share a certain amount of content (libraries mainly, but not JIT'd code). You can't share JIT'd code, because the JIT generated code has specific addresses that are for the use of that program, and you can't guarantee that any two programs share the same address mappings.
A more interesting question is why you can't have a JVM processor or operating system. Indeed, these were tried -- the Java Processor that Sun worked on was capable of executing bytecode natively (and so if that'd been successful, maybe you could have had a virtualised JVM). However, the development of this processor took such a long time that by the time it was done, a general purpose CPU running the JVM compiled for it was faster than the custom hardware that was built to do just that, so it was a commercial flop.
That said, embedded JVMs exist almost everywhere -- on SIM cards, chip-and-pin, in Blu-Ray players -- and as embedded devices need no virtualisation.
Bear in mind that the JVM was created to allow abstract code to run on an unknown processor in the form of set-top-boxes, and that it has become wildly successful in the embedded space -- though the advent of the internet and code-in-browsers made it take off as a general purpose programming language and runtime environment. The fact that it's lasted 25 years and no-one has thought it relevant to add virtualisation begs the question of why you think it's an interesting question to ask?
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…