The safety of references, no raw malloc, no null pointers, compiler-checked thread-safety of types, consistent and enforced error handling help a lot to make robust programs, and allow making bigger refactorings without fear of screwing something up.
The Turing Tarpit means that theoretically everything you can write in Rust you could have written in C, but in practice Rust enables things that wouldn't be worth the risk/effort in C, even when doing a ground-up rewrite.
This kind of attitude only works in an exceedingly small part of the software world that just happens to be disproportionately represented on sites like HN. Elsewhere, it's not a good luck to be using words like "legacy" on a resume without a lot of explanatory text about why exactly it really was legacy and deserved a full rewrite.
I have the same sense as you: when someone tells me they rewrote their company’s “legacy” code, my spidey sense perks up. Now I’m wondering if there was really a good reason or if he just refuses to learn an existing code base.