The Strongest Self-Effacingness Objection

In What's wrong with self-effacing moral theories?, I explain why the basic self-effacingness objection to utilitarianism is no good. But I've recently come to the conclusion that we can formulate a stronger version of the objection, as follows:

P1 (The Normal Competence Condition): Rationality implies normal competence.
P2: Morally fitting agents can be rational (hence normally competent)
P3: A fitting utilitarian agent would lack normal competence.
thus C1: A fitting utilitarian agent is not a morally fitting agent.
P4 (The Truth-Fit Connection): If an agent that "fits" some theory X is not yet morally fitting, then X is not the true moral theory.
thus C2: Utilitarianism is not the true moral theory.

I take P4 to be analytic, and P2 to be uncontroversial (moral virtue is surely not strictly inconsistent with rationality). So that leaves P1 and P3.

Why accept P1 - the "normal competence condition" on rationality? I accept that this is controversial, but it flows naturally from a conception of ("non-ideal") rational capacities as those capacities which render an agent well-equipped to act and function well in a wide range of "normal" environments.

N.B. By "normal" here I mean explanatory rather than statistical normalcy: the sense in which it's "normal" for cats to have four legs, even if a madman has amputated a limb from every actually existing cat. As a heuristic: suppose that there's an a priori objective probability distribution over the possible worlds, reflecting how likely any given world was to be actualized. Perhaps worlds like ours are relatively "probable", whereas BIV and Cartesian evil demon worlds are highly improbable. "Normal competence" would then require that an agent be capable of functioning well across a sufficiently wide range of high-probability (non-wacky) worlds.

On this conception, if an agent is ill-equipped to function effectively even when nothing "wacky" is going on, then there's something wrong with them -- more particularly, they lack adequate rational capacities. (I bracket the possibility of lacking adequate bodily capacities by including one's body type as one of the environmental variables specified as part of the "normal situation". So even a person who actually finds themselves in a paralysed body would not be paralysed in a wide range of normal circumstances, as I'm conceiving of them.)

So, while not obviously true, I think that P1 is at least reasonably plausible (which is more than can be said for most self-effacingness arguments!). One interesting feature of this conception of rationality is that it introduces an element of "relativity": the dispositions and habits of thought that are rational for us fallible human beings may be very different from those that are rational for Martians or gods. But this is plausibly a feature rather than a bug: any conception of "non-ideal rationality" is going to have to be sensitive to such particularities of our constitution.

Assuming we grant P1, then, defenders of utilitarianism are committed to denying P3: the claim that a fitting utilitarian agent would lack normal competence. P3 is most plausible if we accept the standard caricature that a (fitting) utilitarian agent would make decisions by means of an (often misguided) explicit "expected utility" calculation. In a future post, I'll explain why this caricature is mistaken.

But for now I'm interested in what people think of the presented argument. Do you agree that it's stronger (and more interesting) than the usual self-effacingness objections? Has anyone presented the objection in this form before? How plausible do you find P1?