Haskell values are immutable, so it creates a new state on each iteration. Since most of these "game of life" type problems need to touch every cell in the simulation multiple times anyway, building a new value is not really that much more expensive than mutating in place. The Haskell GC is heavily optimized for quickly allocating and collecting short-lived objects anyway.
But yeah, if you're looking to solve the puzzle in under a microsecond you probably want something like Rust or C and keep all the data in L1 cache like some people do. If solving it in under a millisecond is still good enough, Haskell is fine.
Fun fact about Game of Life is that the leading algorithm, HashLife[1], uses immutable data structures. It's quite well suited to functional languages, and was in fact originally implemented in Lisp by Bill Gosper.
But yeah, if you're looking to solve the puzzle in under a microsecond you probably want something like Rust or C and keep all the data in L1 cache like some people do. If solving it in under a millisecond is still good enough, Haskell is fine.