I don't think that our game shows necessarily mirror the dumbening of society, or mirroring it, even. They're fun to watch, and to make it fun to watch, you have to lower the bar to allow people to participate.
Who today would want to watch some yahoo displaying his specialized knowledge on opera, or rocketry, or the mating habits of the condor? What if the difficulty of Jeopardy! clues was such that the $2,000 clue from yesterday became the round one $200 next week, and the difficulty went straight up? My guess is that the ratings would take a nose dive. Even if I don't have a clue about a category, I can still say "hey, that's kinda neat, I had no idea."
It is fun to be right, to be told "good job" even if by proxy. Even $64k Question had the questions for tens of dollars that allowed a contestant to get his feet wet, shake out the cobwebs and to expunge the nervousness. And I would make the claim that knowing about boxing back then could be similar to the Celebrity weeks that Millionaire used to hold, in terms of type of knowledge.
I don't think we're getting dumber as a country, but I don't think we want to watch the tippy top of our society pondering complex equations and reciting Shakespearean sonnets, we want to be able to play along, to say "Haw, I knew it before THAT guy!" and so on. If we wanted to watch the off-the-chart smart people being smart, we'd have College Bowl as a league on par with minor league baseball.