Wow. You're onto something, and rather depressingly so.
There's no shortage of lower- and working-class characters, situations, and concepts that good TV could be built around... so why hasn't it?
Radical (short) answer? Because TV doesn't want to question the false promise of unlimited consumption that it markets through depicting the middle-class fantasy life as not only attainable, but "normal."
Longer answer: the reason lower economic and social classes appear only as sitcoms, as patient-of-the-week on doctor shows, or in fantasized historical or sci-fi locations is because most of the viewers don't want to admit the reality of life for 60% of Americans (the 60% who do not have 90% of its wealth and privileges). I include here not only the viewers who control the bulk of the country's goods, but those who have little, who go largely without health care or good education or opportunities, but have been willing to be convinced that really, they're part of the middle-class - after all, look at that big-screen TV they own. Just like those people in the nice houses on TV. (Never mind that in reality, the TV, pickup, and car are about to be repossessed. And that the lottery will never make you an instant millionaire.)
I think the reason shows about cops and investigators do explore more of the real lives of those who lack financial, social, and/or cultural capital is because cop shows draw a bright line of morality guarding "us" against "them." They play within a stark moral framework in which poverty and its consequences - crime, drugs, mental illnesses, community violence - are so close to evil as to be virtually the same thing. Moral goodness therefore means staying out of poverty. Getting out of poverty is for only the very, very few lucky ones, who work very, very hard. Cop shows always have a few "deserving poor" so we can pretend that anyone who works very, very hard, goes to church, etc., will eventually succeed, and thus if anyone remains poor, it's their own fault.
American cop shows reinforce the social belief that poverty, crime, etc., are the natural consequence of personal moral flaws. That includes the physical failings of the poor (ugly, unhealthy, too sexual, too passive, too old, young, *Slytherin*) as well as "bad families". Far from exposing the root causes of poverty, cop shows simply invite viewers to be voyeurs to this misery, and to sigh with relief at the end that we the viewers are so lucky.
Aaand... Cut to commercial for iPod, vacation cruise, sexy new clothes. Imagine the cognitive dissonance if a show was set in the reality that is life for most people on this planet -- and then every 5 minutes it cuts to 8 commercials in which everybody's young, strong, healthy, educated, well-spoken, clever, sexy, freshly bathed, well-dressed, living in gorgeous houses, enjoying a safe, lovely outdoors, never stopped by cops...
It would look like almost 2 different species - or races - which is what this planet increasingly *does* look like.
Your observation is so perceptive, elf! It gives a much broader perspective to the occasional fandom discussions of class. Hard to deal with it in fandom when our shows, books, etc., don't admit its existence.
Of course, media didn't used to include gays, or many women (other than Mothers, Wives, Virgins and Whores). Fanfic puts them in. Can we do the same for the poor? I believe that's what many in HP have done through exploring characters like Snape (impoverished, violent working-class upbringing), Lupin (unemployed and forgotten by his former school friends), even Dean Thomas or Blaise Zabini (unstable, possibly dysfunctional families).
Compared to a slashy or subversively feminist reading of a mainstream middle-class values text, what does it look like to read through the "lenses of poverty"?