It does seem that poetry has the power to be the kind of moral and political force which Shelley dreamed of it being. The first poem I would point to is Amanda Gorman's piece "The Hill We Climb," which became an immediate sensation. It hit the zeitgeist of the moment among many people because it crystallized both the pain in the nation—from COVID to the invasion of the Capitol to the deep political divisions in the US—and the evidence of hope (even in Gorman's own life story) that positive change is still alive and part of the American experiment. It did everything an occasional—that is, a poem written for a specific occasion—should do by moving the public emotionally and providing a compelling political and moral vision.
Another poem that caught the moral and political zeitgeist of a public moment was Walt Whitman's "O Captain! My Captain!" which expressed the country's grief at the assassination of Lincoln and helped cement him in the public imagination as a great leader.
I would argue, however, that it is the cumulative effect of a whole series of poems—a poetic movement as a whole—that has the greatest impact on the moral and political climate. The emphasis, for example, of the Romantic poets on elevating and showing the good in despised peoples, such as peasants or gypsies, had an effect over time of raising sympathy and political support for oppressed groups. Poetry, too, is most effective when it is turned into songs that can be used as rallying cries.