Your rewrite has clarified the matter significantly, and I now think I follow the core or your question: can it boiled down to something like “If we create a super-intelligent AI and program it to prioritise what we (humanity) want above all, wouldn’t the AI be intelligent enough to be offended by our self-centredness and change that utility function?”?
Others here may be better able to imagine what a self-aware machine intelligence would make of how it was initially programmed, but as far as real-world experience it is currently unexplored territory and I wouldn’t consider anything I can speculate to be meaningful.
I notice that you only compare time spent hand washing to time spent debilitated by respiratory illness, but hand washing also reduces likelihood of other ailments, eg gastric infections due to fecal or other bacterial contamination, and intestinal parasites (especially threadworm if you have kids...).
Even without specific numbers on the time that these might rob you of, hat would seem to push the balance in favour of hand washing.
Apart from anything else, being ill or having a high parasite load is just plain unpleasant, and long periods of illness (even if few and far between) are more damaging to sense of wellbeing than short periods spent on a menial task multiple times a day.