That was Leo Strauss's view, and it's certainly not crazy. But you're suggesting that mere appearances should be kept up (as in civil religions too), that lukewarm faith might suffice because the whole thing would be a sham, a defense against facing the unpleasant truth.
I've written a lot about this esoteric-exoteric distinction. What do philosophical insiders think, and how should appearances be arranged for unenlightened outsiders to sustain society based on noble lies? Is everyone fit for enlightenment or do we prefer our illusions?
These questions go back to the origins of Western philosophy, or at least to Plato. The ancient Greeks had their public polytheistic myths that rationalized their social order (their patriarchy, slavery, sexism, and so on), but they also had their mystery religions which taught a mystical, revelatory form of self-help.
In any case, I agree that a doctrine of double truth may be needed, which is to say that it arises organically because of the differences between social classes.