Is it? I think it's fairly uncommon to use types to enforce correct units in calculations, and you need a pretty sophisticated type system to be able to do it.

I'm not saying it's a bad idea, just that it's not really a core application of type systems in real-world programming practice.

Sure, but the general idea that you should disallow undefined operations are a core application of type systems.

You don't need too advanced of a type system to implement what you're talking about. With the caveat that doing it in Java would make the code tedious to write ;-).