It seems like it's the sort of thing that's useful in something like Agda, where you use the existence of a function (without running it) to prove that its result exists. (The type is inhabited.) Or so I've read; I haven't used it.

But if you're going to run the program, you typically want to know if a function will return promptly, and a total function could still spin for a million years calculating something, in a way that's indistinguishable in practice from diverging.