That British-bad-teeth thing is really an overblown joke, but it can be used to truly funny effect, as in the Austin Powers movies.
It stems (I say) from the advent of widespread colour television, which highlighted the difference between the smiles of Hollywood movie stars and those of British pop stars.
In the Sixties you had Warren Beatty or Robert Redford, with their Pepsodent smiles, the impressive result of expensive cosmetic dentistry, then you'd see David Bowie with his mouthful of drug-decayed gravestones! LOL!
An image that makes me laugh is Clint Eastwood in his legendary spaghetti westerns. Here's this 19th-Century bestubbled drifter, who's never seen washing, let alone brushing or flossing; yet he has a smile (grimace, in Eastwood's case!) that could blind an Eskimo!
(Sorry, we're supposed to call those people 'idiots' or something these days, right?)
Anyways, that sort of dental work wasn't then as popular in the UK and Europe (still isn't quite as big) so even those with money didn't bother sorting out their smiles. Just didn't occur to them.
In America, or more accurately in image-obsessed Hollywood, you just gotta have the bling! smile. It's notable that Tom Cruise was placed under a great deal of pressure to deal with his less-than-perfect teeth, before he secured his starring role in Top Gun, the movie that 'made' him.
I think this is a positive thing. It's true to say that someone with great teeth makes a better impression than someone with yellow, sharp-edged fangs!
As for me 'n' PT, we are British nominally and culturally, but not really ethnically! Our teeth are good but perhaps not great!
TNBT