Not all Americans are particularly political, and those who are tend to be too occupied with bread and butter domestic issues to have any reasonable understanding of great power competition: not to be dismissive of or to denigrate Americans, but most aren't even familiar with the terminology.
You can't reasonably expect the overwhelming majority of Americans — including most elites — to have the interest or attention span to follow what the mandarins governing Beijing are saying, never mind the contextual knowledge for reasonably grasping what the downstream effects will be. Keep in mind that most of our "ruling elites" aren't exactly intellectuals, even if they're compelling enough to get elected.
There are obviously some informed elites in the US when it comes to China; but that absolutely does not mean their voices are heard, assuming they're even able to speak with candor, except anonymously. LOL.
This is in part why it's so easy to vilify countries like China and Russia in the West: domestic audiences on average enjoy limited, if not skewed understandings of "the competition" mostly informed by crude gists and misleading caricatures dished out by entrenched media and established elites.
Not looking to oversimplify in excess, but for the sake of discussion: if there's anything impeding better American policies and responses vis-a-vis the rise of Pax Sinica, it's a lack of political will — rather than stupidity — heavily rooted in the structural misalignments you alluded to.
