Part of the charm of purely functional solutions for me (and why I'm hooked) is that it forces you to think about the representation of the data that you would need in order to have a "clean" solution without mutation. E.g. IntMap for index of arrays and folding with Set/Map operations to build state without accruing algorithmic complexity. I've found that I do a lot more "deep thinking" when forced into using (or creating) the right data-structures and this is something I enjoy a lot more than purely iterative debugging/hacking, and it's more satisfying (to me) at the end of it all.
My go-to for AoC is almost always Attoparsec + Containers with a recursive "solve" function and the complexity seemingly always stays manageable. I'm no savant but feel free to give examples of a tricky task to solve functionally I can share a specific solution.