Haskell needs a GC because it can't figure out whether a closure might outlive any of the variables it references. This can be addressed by a Rust-like borrow checker. (In the rare general case where multiple independent pieces of code need to keep some object alive, this can be done via refcounting which of course is a kind of GC.)

Type based memory management has been done in FP languages. The point is that it completely breaks the experience.