Let's unpack that. You advocate using non-Turing complete languages for things that don't need it. Great. Something like DTrace does not need a Turing complete language and D isn't Turing complete. Awesome.
But then you say that if you're using a Turing complete language, what's wrong if the type system is Turing complete as well?
Well, does a Turing complete language, C or Rust, need or in any way benefit from a Turing complete type system? Does a low level systems language, C or Rust, need or benefit from a Turing complete language?
Other than an implementation pun, I don't see any point in this needless complexity. The point of a type system is safety. I don't see how a Turing complete type system gets you to heaven.