> I am gonna handwave this one slightly because I don't fully remember all of the details, but full program inference and subtyping is undecidable. Rust doesn't have subtyping in general for this and other reasons, but lifetimes do have subtyping. I am sure this would get ugly.

Correct. Haskell is the only language I know of with globally decidable type inference, and uses the similar hindley-milner method as Rust... but no doubt some of Rust's language features can break global inference. In Haskell, many common language extensions can also break global inference.

I think if Haskell was written today they probably wouldn't pick global inference as a goal, Haskell "best practice" types the function boundaries in the same way that Rust enforces.