In fact, I once had an argument in high school with my friend over extraordinary people and ordinary people, Raskolnikov style. At the time, I proposed that some people are by nature extraordinary and therefore the rules don't apply to them, so they can live for themselves. Meanwhile average people should be happy with their lot. It's just the way of the world I said. All those years ago.
While I still do feel some people have an inherent capacity to appreciate culture and experiences that others don't. I realize now, that for many socialization defines their interests more than inherent capacity. So yes we should all cultivate ourselves and get the most out of our every individual experience. But self cultivation shouldn't be the one end goal.
Leonardo DaVinci's qoute is a product of the renaissance, the era that created the cult of individualism. And, therefore, should be seen through that lens. If there are such great things in the world; food that can be savored, music that can move you, art that can bring you to tears, if there are such enlightening experiences available, shouldn't they be shared?
I now think that a sense for the better things in life, can be cultivated in every person. And often it's a question of access not ability. Or at least I hope it can be cultivated in every person. Otherwise the "average" person's existence is doomed to be quite unfulfilled.