The better view of utilitarianism involves leveling up: taking all the warmth and wonder and richness that you’re aware of in your personal life, and imaginatively projecting it into the shadows of strangers.
I would take it further and say that utilitarianism levels up your compassion for both those close to you and those distant from you. By becoming aware of the reasons that were already there, as you say, your appreciation of those reasons can become deeper for both sets of people.
I am not sure whether my worldview is strictly utilitarian. However, my worldview is one that extends compassion to all living creatures, everywhere and at all times. With this worldview, it seems I experience what I described in the latter paragraph.
PaulCousens comments on Leveling-up Impartiality