But since you're the American, can you explain to us humble Europeans what's wrong with this car?
Station wagons (in the style Chase, Karen and S'wellen drove onscreen) were quite common in the mid-1970s. We were all driving larger cars like that with little concern for the price of gas, at least until the second oil crisis in 1979 when gas prices went through the roof. (Obviously these TV characters were rich and no amount of OPEC instability was going to bother
them) The US was already in an economic slump and when OPEC had us by the short-and-curlies, people started looking toward smaller Japanese and European cars. This caused more problems, since the US car industry was intertwined with our status as a superpower. They couldn't just suddenly start making the smaller cars--those take a while to design, and the manufacturing plants would need to be refitted and workers re-trained. Once the Big Three automakers turned the ship around, they were in unfamiliar territory...especially Chrysler, which had to declare bankruptcy and re-organize via government bailout. They didn't go willingly toward smaller cars--they were forced to.
One of the main changes that occurred in the "family car" segment came out of the re-organized Chrysler, which had up to then been most closely-tied to the gas-guzzlers. They introduced the minivan, which they marketed as the successor to the old-style station wagon. It had better fuel economy (though not by much) and many more safety features and lower emissions than a station wagon. It also bridged the gap between full-sized vans and family cars. The more upwardly-mobile yuppies with families flocked to minivans, and thus the people "stuck" with the old-style station wagons looked dated and/or old-fashioned. If you were still driving one of the larger models by the mid-1980s, you were either old (or just old-fashioned) or too poor to afford an upgrade. Many still had to burn leaded gas (thus the "lead sled" crack) and were seen as causing added pollution. Karen seemed to ditch hers around the time she married Mack. It's not that anything was "wrong" with station wagons per se...they just fell out of favor as something new came along.
An argument could be made that the minivan eventually helped Americans transition to SUVs, since they had many of the same advantages that sedans lacked, including that large cargo area in the back that station wagons had. Mack MacKenzie was a trendsetter by driving a Jeep SUV years before they became stylish (and ubiquitous). But then, he married a car dealer, so maybe he had the inside track.