To me, this is the argument for formal verification. I don't want to hear a hand-waving explanation that this algorithm will always complete. If the algorithm is sufficiently complex I want proof. Otherwise, why would I believe you? Abstractions, in the mathematical sense, always hold (unless there is a flaw in the definition itself). Axioms in any sense are always going to throw a wrench in things. Thank Godel. But…
Formal verification is nice, but requires crazy skilled people at high cost. It's not always practical/feasible to have as part of your SWE process.
It's nice to have when it is though.
The cost is coming down. Proof automation is incredible today and rapidly improving. This is the part that does the tedious parts of a proof for you so that you can focus on the theorems that matter. The languages and proof systems themselves are easier than ever to pick up and use which is bringing the skill cost down.
I don't think most software projects need a huge, dedicated team of specialists to benefit from formal software verification.