Arachnophilia, here is a sort of counter to the idea that your cats are sacrificing to you. Dogs do this too, and dogs are pack animals - admittedly, cats less so. So it may be that they are wired to bring some of the prey back to the pack, or back to the pack leader.
But I think this is an angle worth exploring. I was watching some footage of wolves in Canada that included a discussion of submission signals, in which one wolf rolls over and exposes its throat to the pack leader. This defuses tension within the pack and makes it more stable.
Furthermore, this has to be in some sense chemical, I would expect. I doubt wolves have a consciousness that rationalises the social contract, as it were, and formulates strategies for the good pack society. But a "submission reflex" may make evolutionary sense.
What if there were a submission reflex in humans? It is common for authority structures to demand that subordinates adopt certain postures, or not make eye contact with superiors. I sometimes wonder if "bow your heads in prayer" is not actually something rather like rolling over and showing your throat, and if obliging people to adopt the position can trigger a positive feedback loop that releases "submission chemicals" or similar.
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