Part of what Koka's functional-but-in-place system relies on is the Perceus program analysis, which, as I understand it, is kind of like a limited Rust-like lifetime analysis which can determine statically the lifetime of different objects and whether they can be reused or discarded or whatever. That way, if you're, say, mapping over a linked list, rather than construct a whole new list for the new entries, the Koka compiler simply mutates the old list with the new values. You write a pure, functional algorithm, and Koka converts it to the imperative equivalent.

That said, I think this is somewhat unrelated to the idea of making linked lists disappear - Koka is still using linked lists, but optimising their allocation and deallocation, whereas Haskell can convert a linked list to an array and do a different set of optimisations there.

See: https://koka-lang.github.io/koka/doc/book.html#sec-fbip