No, this is the technique we use in practice in formal methods to prove program properties. When we write a program correctness proof in TLA+ or Lean, this is what we do. This is also how we build invariants into languages. When you learn how to write formal proofs and design type systems, this is what you learn.
> Rust, however, can maintain invariants and be expressive enough because it relies on outside the computer assistance (aka unsafe blocks).
Rust maintains its invariants by making a stronger invariant inductive in the language.
> Google mentioned they had little problem getting people to work with Rust.
I am not talking about Rust in particular. I'm talking about your general point that more soundness is always better, and your claim that my argument is an example of a nirvana fallacy because I compare an imperfect solution to a hypothetical perfect one. I am trying to explain that we know that more soundness is sometimes worse for correctness in practice. The problem is not that more soundness isn't perfect, but that there are currently better solutions than more soundness in some situations.
You seem to be unaware of the shift in software correctness since the seventies. The gap between the size of programs we can prove correct using deductive methods (currently ~10KLOC) and the size of programs produced in industry is only growing. That is why there's been a shift from deductive proofs to methods such as concolic testing (e.g. KLEE). You can see that by looking at the programs for any software verification / formal methods conference.
To be clear, I am not saying that more soundness is never better; I'm saying it is sometimes worse. You can say that we should use ATS more, but the effort of producing software that's proven correct with ATS is not justified by the additional correctness guarantees you gain. I.e., at some point you pay $1000 for improved confidence worth $100.