Well yes, if your teeth are yellow it can look bad, but from what I gather gleaming white seems to be the acceptable level to those in the US concerned with such things.
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"Gleaming white", is, IMO, overkill and, IIRC, actually unhealthy, depending on the method by which said whiteness is procured.
Anyway, the root of the stereotype is apparently from WW2, where a lot of US soldiers will have mixed with a lot of British soldiers, many from lower-down the social ladder. Then add the fact that Britain had been under seige for a large portion of the war and it's easy to imagine that at such a time dental hygiene was not amazing amongst the aforementioned British soldiers.
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Yeah, getting bombed to oblivion and back is going to pretty unhelpful for dental, or really most forms, of hygiene.
(Although I stopped brushing them after one collapsed into itself...now I can't eat anything on the left side of my mouth...)
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So, let me see if I've got this right: you were brushing your teeth, and then one of your teeth 'collapsed' in upon itself, presumably becoming a small nub of enamel that is embedded in your gums?
I think you may need some serious dental help.