Fathers, it seems, are either made absent in TV families (eg The Gilmore Girls) or are portrayed as harmless buffoons (The Simpsons, Malcolm in the Middle, Everybody Loves Raymond). It's hard to think of a single example on TV today of an intact family in which a father exercises a wise and protective paternal authority.
I don't think this is accidental. Paternal authority is fixed and unchosen, and therefore runs counter to the liberal principle that we should choose for ourselves according to our own will. Liberals are more comfortable with forms of authority with which we can "contract," or give individual assent to. We simply don't "contract" to place ourselves as children under the authority of our fathers: it's not something decided by individual will at all, but rather by the chance of inheritance.
Even in the nineteenth century you can find signs of a discomfort with the idea of paternal authority. Even the generally conservative Jane Austen often portrays both Anglican ministers and fathers as vain and inept (Persuasion, Pride and Prejudice).
American popular culture seems to have preserved the conservative ideal of fatherhood for the longest time. There was a very popular series of American films, made mostly in the 1940s, called the Andy Hardy series. The father in these films, Judge Hardy, is a very traditional representative of fatherhood: in sharp contrast to modern entertainment, it's the teenage son who provides the comedy, whilst the father provides knowing guidance.
I have (vague) memories of watching American TV shows of the 1970s in my childhood, such as The Waltons, and Little House on the Prairie. My recollection of these programmes is that the fathers were strong and respected by their families, whilst the mothers were lovely and maternal.
But American popular culture no longer redeems itself by presenting such positive images of family life. There are even some male scriptwriters who are getting annoyed by the relentlessly negative image of fathers on TV. For instance, veteran Australian television writer, Bevan Lee, says,
My personal idea of TV viewing hell is these (dopey dad) sitcoms, things like Everybody Loves Raymond, Home Improvement, Malcolm in the Middle, where the father figure is a central figure running around like an idiot, and he's the butt of everyone's jokes. It's my idea of The Hague war crimes torture to tie me to a chair and make me watch those on loop.
Similarly, Queensland University television course coordinator, Alan McKee, complains that,
In the last 10 years there have emerged new representations of families where the characters, the dads in particular, are incredibly flawed - to the point of being moronic. The kids are often terrible to point of demonic and mother is strained to the point of hysteria.
It seems that some people in the industry recognise the problem, but their solution is not too promising. They want to replace the "daggy dad" with the "complex, damaged, dramatic dad". Thus script editor Diane Cook believes that The Sopranos is a turning point in portraying a more "engaging" father figure (a mafia mobster) who is "conflicted" and has "deep and complex feelings about family and fatherhood."
And similarly Neighbours script writer, Luke Devenish, says that the show's "daggy dad" prototype is being left behind, with the reintroduction of a founding character, Paul Robinson, described as follows,
The character is desperately trying to pick up where he left off, with five children by three failed marriages, carrying the baggage of a murder, time on the run and a jail term, as well as the stigma of three divorces. It is a coming-of-age for fathers on the show, and something of a turning point for them in Australian soap history.
I'm not sure which is worse: to be portrayed as harmlessly incompetent or to "come of age" through divorce, murder and imprisonment. Either way it seems that there is still no room on TV for a moderately competent, respected father who lives together with his own family.