I don't think one can even compare Kodachrome with 78 or 16rpm records, as the basic machinery to manufacture and play them has been in production. There are still 78rpm discs being manufactured and turntables to play them. If someone decided to release a 16rpm disc it would not be unreasonable to cut a disc to play at this speed. It would not be too difficult to modify 45/33 player to play the disc either.
With Kodachrome, the biggest problem I see is the processing.
With B&W, E6, C41....Kodak have managed to alter their manufacturing process to include shorter runs. This has meant Ektachrome (hopefully) and P3200 can come back. I am not one of those people who throws my toys out of the pram because a product is a little late to market. Ektachrome is highly likely to hit the shelves this year. So, though it would be more costly and difficult....in theory Kodak could make a run of Kodachrome film. But who is going to process it?
What could keep B&W, E6 and C41 alive (albeit at much increased cost) is that they can be processed at home or by a cottage industry lab. In the "almost worst case scenario" where all the mini labs have shut and nobody is offering E6 processing by lab any more.....serious enthusiasts can still process the film at home. That is impossible and always will be with Kodachrome.
The days when National Geographic went through hundreds of thousands of rolls of K'chrome a year are long gone. They went digital years before K'chrome was axed. They're not going back. Demand might conceivably be higher than in 2009 but it's still not enough to make building a new K14 processing machine. It's nowhere near. So even if someone could manufacture Kodachrome, there's no way of processing it. Demand isn't sufficient to justify the millions it would cost to build a machine, house it, operate it....the machines were designed to be run continuously....one cannot let it sit for a few days then do a run....the chemicals will go off. K14 made sense when everyone shooting movie film preferred K25 and K40....and when K14 was the stuff of choice for Nat Geo and many slide photographers. Sadly, as much as I miss it, it doesn't make sense now.