Right, I think you only need monadic bind for semantic predicates. Ordinary semantic actions (i.e. ones that don't feed back into deciding how to parse the rest

Right, I think you only need monadic bind for semantic predicates. Ordinary semantic actions (i.e. ones that don't feed back into deciding how to parse the rest of the input) can fit smoothly into a parser combinator design without monads, but AFAIK that's not how it's usually done.