It's kind of interesting when you mention it.
I Love Lucy or Andy Griffith are iconic shows. Yeah, they may be fading into the past just a bit but so is Wizard of Oz.
With All in the Family or Happy Days those items were entered into the Smithsonian right after their hay day or, in Happy Days case, I think while the show was still on (Fonzie may have already left at that point). The point is, that everyone thought that the chair and the jacket belonged in there because they were both iconic pieces of American pop-culture. They didn't last very long. Both shows kind of fell off the radar shortly after they were canceled. You may still hear of people who will talk about I Love Lucy or Andy Griffith (even that is starting to fade) but the drop off both both All in the Family and Happy Days happened a lot sooner.
The biggest reference to Happy Days today is "Jump the Shark" but, even then I don't think most people under 35 would have much of an idea of the reference without looking it up. To me, in retrospect, Archie's chair nor Fonzie's jacket really belongs there. They don't do any harm by being there but they also really don't really live up to the iconic status that people thought they had.
Good analysis. Interesting perspective on the impact and longevity (or lack thereof) of those shows in reruns.
I think that it is worthwhile to note the important turn in television that All in the Family represented in bringing social commentary so front-and-center, but I also think that that played a part over time in its becoming more stuck in time than the others. Perhaps likewise Happy Days, but less for the social commentary than its period references to the '50s, which had more meaning for boomers than others.
I Love Lucy and Andy Griffith, however, had the good sense to keep plotlines more universal, which, I think has given them legs, particularly for Andy Griffith, which I think was almost always written as a morality tale for the everyman.
I remember reading that Robert Reed ("Mr. Brady") always argued with producer Sherwood Schwartz that The Brady Bunch should deal more with current trends and topics. The time period was 1969-'74, during which war protests were going on and the women's lib movement was big. Sherwood and his son, Lloyd, who worked together on the show, made the conscious decision to keep current news and topics out of the show, and instead to focus on traditional family issues and things that kids dealt with. They knew that they planned later to syndicate the show. They proved to be right, as it became one of the most highly syndicated shows of all time. Kids of later generations identified with the characters, even as the clothing and set design showed its real age. Of course even that evolved, as the kitsch factor of the show's '70s culture and fun made it something to ridicule -- but even that was done with more fun and a sense of knowing the characters. Which, I think, is the point.
When the writing is good and the characters deal in universal truths or universal problems, the shows are more likely to survive for generations. And people will recognize good writing.
As for Andy Griffith and I Love Lucy and other genuine classics, I think that is the reason that they have had longer legs than most, and especially Andy Griffith, will survive. The thing that I think is hurting the classics the most today, however, is the reluctance of TV networks to show anything that is (a) in black and white and (b) not filmed in widescreen. (The '50s and '60s old shows, ironically, DO hold up better for HD than later reruns, because the older ones were usually FILMED, as opposed to videotaped as was popular in the '80s -- and film is already HD by definition.) So, I think that although they often look stunning on HD TVs, they are not wide-screen; so many networks, like the Disney Channel, simply won't show them. Of course, also like the Disney Channel, there are other reasons that they choose (wrongly I think) to leave out the classics, but I do think the screen dimension works against the classics, unfortunately.
And to bring this back on topic, I think that the theme of COP is a classic, something that is universal: progress. Right now it is stuck in time, but the theme of seeing how progress has changed things and portends for the future, is still a good one.
Its relevance to the NY World's Fair and the optimism of the '60s make it a good candidate for the American History at the Smithsonian, but it is and even better candidate for Walt Disney World... where it not only ties in with the genesis of EPCOT, but also, with proper care and updates, can still tell the story of human progress and optimism, even if it comes with a nod to the past.