I don't know if that's always the case. My understanding is that TLA+ is really designed to prove properties about algorithms. Knowing that complex algorithms are correct is very useful eventually if it doesn't provide a correct implementation in a real world language.
But TLA+ is a bit of an unusual proof language. I think most of them are like you describe: SPARK, Dafny, F*, CBMC, all the Rust ones, etc. I'm not sure about the interactive proof languages (Coq et al), they are too complicated for my normal sized brain.
Yes, and making those languages (SPARK, Dafny, F*, CBMC,....) more widespread, the kind of something that everyone expects to be out of the box on their favourite language is how this can eventually gain more adoption, than a few selected companies, or academic research.
But TLA+ is a bit of an unusual proof language. I think most of them are like you describe: SPARK, Dafny, F*, CBMC, all the Rust ones, etc. I'm not sure about the interactive proof languages (Coq et al), they are too complicated for my normal sized brain.