Desiderata for a theory of atonement

My previous post on atonement implicitly identified one constraint ("must") and one desideratum ("should") for a theory of atonement:

1. The theory must be able to apply in cases where the person saved lacks personal sin.
2. The theory should not require explicit beliefs on the part of the person saved.

There is another desideratum that I think is important but somewhat vague:

3. At least one of the facts that Jesus Christ actually lived among us, died on the cross and rose again should in every case be central to the mechanism of salvation.

This condition rules out theories on which the mechanism of atonement is that we are transformed by the example of Jesus Christ (this will be a subset of what my previous post calls "epistemic theories"). For in those theories, the central part of the mechanism of atonement is not that Jesus Christ actually lived, died and rose again, but that we believe that Jesus Christ actually lived, died and rose again. The reason Jesus Christ had to actually live, die and rise again is not for the mechanism of salvation to work, but only because God is not a deceiver and so God could not teach us that Jesus Christ lived, died and rose again unless this was actually true. But the soteriologically important thing on such theories is the belief that this happened, not that this happened. And hence such theories are unsatisfactory.