If the VM was independent of CIL, what would it depend on? Aren't you just proposing to create a new intermediate language, along with a translation layer from the old CIL to the new language? I don't see how that would solve anything.
If you're creating something new, it makes sense to think about how to design it to make it flexible in the future (but making it more flexible is not always the right choice).
But if you already have something as big as the CLR, significantly changing the design should only be done if it actually provides significant benefits, not just when it might provide some benefit in the future.