First of all, I think that "premeditated" viewing will lead parents to being more selective and thoughtful in their and their children's viewing time. If you have to go in search of it, you'll probably think about whether you really want it first.
Second, it allows parents to screen shows ahead of time for content. Not sure about the propriety of a show? Now you can watch it first and decide whether it is appropriate with all the information at hand.
Third, in a word: advertising. When you prerecord, you have the power to skip the ads altogether. We all know that advertising is an annoying waste of time (ahem, except during the Super Bowl ; P), but it can also seriously compete with values parents try to teach their kids. I have actually seen advertising for erectile dysfunction medication and condoms during children's programming. And all the ads using scantily clad, seductive models to sell products air with family friendly programing too. Personally, I'm not ready for my toddler to be exposed to that.
Moreover, marketing firms know (and do studies on it) that marketing to children works (Beder, 1998). Not only do they have their own buying power, but they can persuade their parents to make purchases, and marketing messages absorbed in youth form children's future buying habits. The average American child sees 20,000,000 30-second ads every single year, and that doesn't include billboards, the grocery store, magazines, or the Internet--just television (Herr, 2007). How can a parent hope to compete with that? And research seems to suggest that the ubiquitous marketing of unhealthy foods to children contributes to American children's poor eating habits and overall health. Some even theorize that the current generation of children may be the first to face a lower life expectancy than their parents in several generations (Kunkel, McKinley & Wright, 2009).
Fourth, I think it encourages family viewing. With the proliferation of entertainment media in our homes (some 66% of American homes house three or more television sets), it has become increasingly easy for family members to spend time at home without interacting. Even when everyone is sitting together on the couch, one member may be texting, another working on homework, a third listening to music, and another surfing the Internet, all with the television on in the background. It's a situation that is not conducive to family interaction. If multiple family members watch and pay attention to the same TV show, it gives them something about which to converse later. According to CSU Northridge (Herr, 2007), the average parent spend just 3.5 minutes per week in meaningful conversation with their child. Surely increased time spent in a common activity could increase that average!