I disagree that it is confusion on my part (I mean, I am certainly confused, but not, I think, about what you said). Your (1) and (2) seem irrelevant since I am talking about the personal EV calculations of individual actors, not global EV. (3) is the point I am trying to handwavingly describe a way of skirting. But it sounds like I didn't communicate it well (or I am wrong about not being confused also, in which case, fine, can't do anything else anyway).
Yes, of course rational agents can account for private information. I am trying to describe a case where a strategy cannot be rationally justified, yet is a better strategy than others because of "having faith in yourself". Now you can always try to flip this around and say: "well maybe the internal calculation that they do involves having evidence that they ought to have faith in themselves, like past success, consistently good mental models, a model of how faith helps, etc". And I'm not talking about those: I'm talking about cases where there is not a good argument, even in an internal calculation using private information, why a person should have faith in themselves, yet doing so anyway helps.
Basically it seems like there are cases where believing that something has a more-than-rational chance of working makes it more likely to work because of the power that irrational faith in yourself provides. But suppose you tried to quantify it: okay, an irrational faith in yourself makes you, I don't know, 20% more like to succeed, so you can account for that. But now it's not an irrational faith, it's a rational one, so you can still have more irrational faith than that, and it can still have the same effect.
My pattern-matching brain says it has the form of a Halting Problem/Godel-incompleteness-type theorem for rational calculation. Roughly: "It is possible to construct scenarios in which non-rational strategies lead to improved success in ways that rational calculations cannot account for."
This would not apply in a toy problem where the range of strategies are completely mathematically known: if all outcomes can be understood probabilistically then it doesn't apply. It applies in cases that are more like: some outcomes are unknown and the probability distributions of them are shielded behind "unknowable information", like new ideas that you have no way of being sure of the existence of. In these cases an irrational belief that you can find a new idea can improve your EV even though there is mathematically no way to justify it, because you can't really model "the probability of finding a new idea" without actually knowing what the idea is, even hypothetically.