I think there is a difference between the morality of a culture and the morality of a political system. I can’t imagine anyone seriously arguing that our culture is morally superior; indeed, the opposite. We have the freedom to be degenerate and, by God, we have exercised it.
But there you have it. The singular American assertion is that THE PROPER DOMINANT POLITICAL VALUE is not “morality”, nor “justice”, but liberty, and that political systems which have sought morality have historically produced oppression, and that these shores are a refuge from said oppression. The cost of freedom is the possibility of decadence.
The American assertion is that the morality of a political system is judged by the degree of individual freedom it affords. By this standard we assert our political system — not our culture — is superior, and the truth of this assertion has been exonerated by the tens of millions of immigrant feet, the “…poor and huddled masses, yearning to be free…” for 250 years.