Haskell specifically is a poor choice of language here, because it creates cycles like the pest. (This is because it uses lazy evaluation, and programming patterns (design patterns?) using lazy evaluation tend to use cyclical references. Strict FP languages might support your point better, but then Ocaml again doesn't work because it
mutates like the pest.)
Furthermore it also allocates like the pest: busy Haskell programs regularly allocate on the order of 1GB/sec. However, this works out fine because the majority of those allocations are short-lived, hence become dead quickly, hence a GC that is designed to only touch live data (like Haskell's GC!) will handle that well.