require that the crate content match the [commit] hash.
If you want to audit a crate, you don't need to require that it "matches" anything else, you can just audit the crate. Download the source tarball from the same URL that Cargo would and audit it. I think the problem with crates.io is that it just gives you the GitHub link (possibly misleading - bad!) and doesn't just give you a button to download or browse the tarball that Cargo actually uses (what you see is what you get).
Defining "matches" and enforcing it against a remote Git repository is non-trivial. It gets worse with NPM because those packages are sometimes the output of the Typescript compiler or Webpack, so now you need reproducible builds (a huge task) and a CI infrastructure to validate them. Nuget distributes .dll files, which often aren't even open source. There's no hope to enforce a correspondence with a Git repository there. A developer who wants to audit a Nuget package has no choice but to decompile it.
NPM clearly has a malware problem, and Cargo will eventually have one because it really wants to be like NPM. I'm not convinced that what you propose is the solution.