I don't think generally it's to show how important they are, I think it's just selfish, egocentric behavior that has become normalized.

In part, due to the heavy marketing culture... and a culture which has low social bonds, where TV and movies are the major social glue.

Whenever I am in a restaurant or public place anywhere in the world, the loudest people tend to be Americans. They simply don't understand the notion of lowering their voices in a public place. I have asked a few to kindly lower their voices and usually get a look of shock...and often some insults in return (read--> absolutely clueless and self-entitled "I will talk as loud as I want").

Putting one's shoeless feet up on chairs, dressing like you've just rolled out of bed or from the gym, letting your kids run around like it's a playground... I see all of these as similar borderline narcissistic behaviors.

Usually Americans get super bent out of shape when anyone criticizes anything about the US (always found this odd... as most countries enjoy criticizing their own citizens' behavior... lest I digress into a discussion of exceptionalism...)

Of course, this is a general statement... not all Americans behave this way. But there is definitely a cultural element... and not one that is well regarded elsewhere.