I don't think anyone shouldn't should. You should should if you choose to should!
What a weird word.
I just don't think *shoulding* is effective in getting the results you want. In fact, I think it's really effective at getting the results you DON'T want! *Needs", too, another word used in the OP -- I have very few needs: water, food, shelter, and maybe one or two others -- and everything else is a preference.
As for "sacred duty," well, that might work on some people, but for me it inspires a great big "feh" of dismissal. I suspect the same is true -- dismissal or resistance -- for others around here.
If your really want to be effective in getting the result that people born in richness/and or happiness are making a greater effort, I think it would be effective to (but I don't think you *should*
) demonstrate how that would be a benefit to the rich/happy person. Inspire them. There is an abundance of benefit and inspiration available in what you're suggesting, so you shouldn't run out any time soon!