I'm not so sure there's a huge "cultural" difference between the U.S. and the rest of the world regardless sleeping in airports (whether overnight or in a lounge). I think the key difference is that the US hubs are less likely to connect long-haul to long-haul than some of the major Asian and European hubs. Also, American airports seem to schedule fewer middle-of-the-night operations and have fewer late-night to early-morning connectors. (Not saying they don't exist...just fewer.) Finally, Pricelining an airport hotel in the U.S. is nearly always cheap.

All of these combine to make airport sleeping somewhat of a rare occurrence in most places. That said, I can see LAX being one place where it's less rare. I don't think it's firmly ingrained in our culture as good or bad...it's just not a common thing.

A quick nap in a lounge? Set your own phone alarm and sleep in a chair...no one will bother you.