I do not believe that the majority of Americans today believe that there is any "moral" purpose for the American government to exist. The left wing sees the US as a fundamentally illegitimate country founded by the dual sins of slavery and genocide that should be improved by dismantling its own myth structure and importing as many foreign cultures as possible to supplant whatever came before. The right wing is only interested in the existence of American hegemony insofar as it can use it to crush its cultural enemies or enrich itself, and is happy to violate by theft or violence any American principle in name or in spirit so long as there's good short term gain.
Neither is thinking of the Nation as an aesthetic and moral project to advance the state of mankind under God, or even Science, or Human Rights, which was how its founders explicitly thought and wrote about it.