Thanks, and yes that makes perfect sense. It's a useful way to think about the problem space.

And then it does lead back to your "????" - which presumably represents the answer to the question of "What's the simplest abstraction that allows one to build a "Parser" (would this still be using combinators??) that is powerful enough to parse regular languages, but, by design, not powerful enough to parse context-free languages?"

Yeah, exactly. I don't know what it would look like. It would be nice if the answer was "functorial", since that's at the bottom of the functor-applicative-monad hierarchy, but functor doesn't provide any way to actually combine the combinators, so that's out.