If you look at history - events, trends, culture - what are the biggest things of which one can say, that only happened because the idea "utilitarianism" existed, it wouldn't have happened otherwise?

If Jeremy Bentham had not come up with utilitarianism, I don't think classical liberalism as we know it would exist today. He came up with a remarkable number of what we now consider "right" answers in the social sciences. And he obviously influenced plenty of important folks, including e.g. John Stuart Mill.

If that hadn't happened, I think other ideas would be more important instead, e.g. natural law and perhaps some vague appeals to egalitarianism.