A couple of thoughts:
Obsolescence can only be reached when there is no utility left in a product. A good example of this would be the minicassette, because when other options were introduced, there was no desire for tape hiss and limited sonic range and thus found itself without much going for it -- including a market. Kodachrome is a vintage technology with a perception of utility by a group of consumers. Those utilitarian merits which advance its utility as a film that continues to be used are novel, unique, and difficult (if not impossible) to replicate with other technologies. If there was no interest in this distinctive mode of reproduction, then it too would fall by the wayside of the minicassette.
Every once in a while, a technological offering long outlives its intended market because a demand continues for a unique characteristic. Often, it makes no logical sense because it's a matter of emotional senses being appealed to. Some things that come to mind which one might call "vintage" yet are still used by many: Spam (the canned meat); the Porsche 911; the Kitchen-Aid mixer (or the Kenwood, either way); the vinyl record; Coca-Cola; Levi's blue jeans; and so on. Under the rubric of considering Kodachrome "obsolete", these too are equally so. Some of these, of course, have been refined over the years as a condition of continuing to offer them to a consumer base that continues to demand them. So has Kodachrome. K-14 is just the third major chemistry solution for the process. Perhaps there's an ecologically sounder way to try a "K-15" system should consumers continue to ask for it by name. In other words, there is still room for refinement, optimization, and streamlining for how it reaches the consumer's hands.
And while I see what you are saying about the Edsel, the analogy still doesn't work. The Edsel wasn't so much an obsolete technology in its day as one which missed the target of what consumers in that day wanted in a car. It was aesthetically unattractive, though built on the same technology as other Fords of the same era (the way a Mercury, which is no longer sold in Canada, is today). GM was still setting design trends under Harley Earl's watch, and people wanted that stylish design, leaving Ford scrambling to find something that was desirable without reinventing the wheel. Eventually, they figured it out by doing the same thing to a Ford Falcon, which came to be known as the Ford Mustang. (I've come to know this stuff, all thanks to a seminar in North American automobile history I learnt at university, yay).
In any event, Kodachrome can be a viable product still, owing to changes in how it is produced, marketed, and made available. Kodak could have an instantly recognizable web store the way Apple has done for a decade and offer Kodachrome direct to consumers the way Apple has offered select products exclusively through their web site (which do not appear in stores). If all demand were absent, then yeah, forget about Kodachrome. The trick is to find the path that can make it profitable. It remains a product which, in effect, is as signature as Burger King's Whopper, or Chanel's No. 5, or Chevrolet's Corvette, or Buckley's Mixture (it's a Canuck thing the Yanks here might not understand). How practical these are or aren't isn't the point: people still want them, even if they've been refined. Likewise, people still want Kodachrome. Without it, what does Kodak have left which emotionally resonates with consumers? Ektar? Sure. What else?
Actually, I think the Edsel analogy was correct. Depending on how one was to read Alan's comment, one could assume that he was talking about calling Fuji and asking them to make Kodachrome. Also, in this case, the Edsel analogy does not mean "discontinued", but "obsolete technology", which Kodachrome obviously is. That is not to say that Kodachrome is not useless (I use it myself), but that the technology is outdated and when Kodachrome dies, K-14 dies.
