And there's a very real danger of this being a fully general counterargument against any sufficiently simple moral theory.

Establishing a lower bound on the complexity of a moral theory that has all the features we want seems like a reasonable thing to do. I don't think the connotations of "fully general counterargument" are appropriate here. "Fully general" means you can apply it against a theory without really looking at the details of the theory. If you have to establish that the theory is sufficiently simple before applying the counterargument, you are referencing the details of the theory in a way that differentiates from other theories, and the counterargument is not "fully general".