I think you are trying very hard to disagree on basic stuff that works very similarly across different language ecosystems, and (looking at other responses) that you're very angry. Disengaging.
The Rust compiler/language has no notion of semver. Saying "Rust is unstable b/c semver blah blah" is a tad imprecise. Semver only matters in the context of judging API changes of a certain library (crate).
> The only reason to do semantic versioning is compatibility
Sure. But "compatibility" needs to be defined precisely. The definition used by the Rust crate ecosystem might be slightly looser than others, but I think it's disingenuous to pretend that other ecosystems don't have footnotes on what "breaking change" means.
I think we're mixing 2 things here: language backward-compatibility, vs. standard practices about what semver means for Rust libraries. The former is way stronger than the latter.
I think the precise pre-condition is that the theory should be recursive, which means either a finite list of axioms _or_ a computable check to determine whether a given formula is an axiom.