It's a class thing. Like the previous scene where Noa dismisses a candidate out of hand for not wearing a suit, it thoroughly anchors the protagonist in a time, a place, and a subculture.
Americans were very conscious about dental care (and still are), because it's a matter of conspicuous consumption. Anyone without perfectly straight and shiny teeth obviously comes from an impoverished background. Good parents don't let their kids grow up with crooked teeth, unless they simply can't afford the dental bills. My teeth are pretty crooked, and it's been pointed out more than once as something that has held me back (always, always after the fact). A friend with similar childhood circumstances ended up getting his teeth straightened in his thirties, simply to have better prospects in employment and romance. Can't say it isn't tempting.
And as this growing trend of the 20th century turned into an obsession, there were the British, not giving a fuck, smiling, even on television, with disjointed dental horror shows between their lips. It became a meme.
Eventually, of course, nationalized healthcare wins the day and it wouldn't surprise me at all if British teeth are, on average, much nicer than American teeth these days. But it's not really about them, and it never was. It was about filtering out yokels from West Virginia who don't have five thousand bucks to drop on their kids' orthodontists. Jokes about the British were just a collectively comfortable way to reference the class disparities within the United States. We say, "haha, English teeth are crooked," and lower class fellas learn to smile with their lips closed.
In a hypothetical LA-based fanfic, where Noa contends with the progenitors of the Runaways (outmaneuvering time travelers in court, wouldn't that be fun?), the anchors would be different. Wearing a suit would be far less common than in New York City; maybe even forgivable for an interview with a law office? The outfits would be more colorful, at least. And the judgments on personal appearance would only start with the teeth. Everyone who isn't pretty enough for television sticks out like a sore thumb in certain parts of LA County, especially if they're under thirty. If you ever want to feel like the ugly duckling, go spend a week in North Hollywood or the other nearly-affordable neighborhoods within commuting distance of the major studios.
All this to say: sorry, couldn't think of an orthodontist-based mini-fanfic for this chapter. The well's run dry.