This is an enormous question. Whatever answer given, the effort of answering is in danger of straying into a realm of the thoughtful, insightful, etc., but it will be subjective and speculative rather than something concrete, resting on a solid foundation.

First, we need to sort out the players. The "folk" are the ones who tell these stories, but that is not where almost anyone has heard them, because the modern world has been fed a perception of American folklore by corporate/media interests. The stories were co-opted by commercial interests and the media to digest, reassemble, and then make available to a larger American public.

On top of this, stories like those about Paul Bunyan were manufactured completely (or nearly so). This inspired the American folklorist, Richard Dorson to term such faux expressions of folklore to be fakelore (1950), a condemnation intended to identify and separate those elements of culture that pretended to be genuinely traditional but were not.

Whether "fakelore" or real folklore, the packaging of these stories by mass media fitted into whatever agenda those corporate interests had/have. That process reaches beyond traditional folklore studies, and perhaps someone could answer that aspect of this process - from the point of view of the history of corporate/media adoption of folklore/fakelore motifs for their own agenda. I am not prepared to answer that, but an answer must consider this relationship between folklore and commercial interests.

Fortunately, the folklorists Michael Dylan Foster and Jeffrey A. Tolbert have given us some excellent tools to begin to address this process, coining the term "folkloresque" in their book, The Folkloresque: Reframing Folklore in a Popular Culture World (2016). The Folkloresque provides a less judgmental path (replacing Dorson's "fakelore") to put one's arms around a range of cultural expressions which coopt or imitate folklore. Paul Bunyon becomes the folkloresque rather than fakelore, because the Bunyan cycle of stories were invented in imitation of folklore. Similarly, Disney's celebration of aspects of American folklore remove the original tradition - sometimes distantly removed - from the original folk roots, and this too becomes the folkloresque. We need, consequently, to consider the motivations and effects of these corporate processes more than we need to evaluate the folklore itself.

Let's also understand the "tall tale": while not unique to the US, the tall tale was glorified on the North American frontier and has become intimately associated with people's perception of the West. It is not so much American as it is Western, and yet the corporate/media interests have repackaged the genre and fed it back to America at large.

One could argue that the tall tale was perfect for America because of the way it celebrated a larger than life view of the world and what was possible. It does seem uniquely American - even though it is not in its origin American (after I finish this, I will attached an excerpt of a book I am currently writing about the folklore of the Wild West).

All this has resulted in a perception of American folklore rather than anything that is truly the lore of the American folk. We can attempt to understand what that original folklore says about Americans and what its effect may have been. Or we can do the same for its corporate coopting of American folklore for mass media, but that is a different process.

Either way, the process of speculating about the answer is too subjective for my tastes. Understanding the parameters of the subject is important, however, before launching into speculation about meaning and effect.