One reason it may never have caught on is that, as far as I can see, very little thought has gone into original bike design which takes full advantage of chainlessness. They are just normal bikes but with shaft drive instead of a chain, so there's no benefit to trade off for the extra weight, loss of efficiency and extra difficulty in mending p*nctures. The classic 'solution looking for a problem'.
However, there is at least one problem that chainless bikes might be a solution to - One of the main reasons why I bought a folder was to stop chain muck getting all over me and over Mrs J's car from having to remove and refit wheels when I carried a full size bike to commute the few miles between her work and mine. I chose a Brompton over other options in large part cos all the mucky bits end up in the middle out of the way.
So there's a potential market with people like me for oil stain free chainless folding bikes, especially if you can make a realistic claim of 'maintenance free'. Run the shaft drive inside a single-sided chainstay and you deal with the wheel removal problem and add very little extra weight. Go for a single sided front fork too while you are at it and you could have a very narrow folded package.
Single sided chainstays and forks would make a lot of sense for making p*ncture repair easier on full size non-folding bikes too, especially with hub gears. Although there's no reason why it couldn't be done with chain driven bikes, you don't get the 'clean' benefit unless you fully enclose the chain. That always seems to look old-fashioned and even if you get over that it must result in a necessarily chunky appearance. This would be even more dominating on a small wheel folder and you wouldn't get such a potentially compact fold as you could with a shaft drive.
There are people who would trade some efficiency in return for perceived style points or who would be unconcerned about maximising efficiency if there were other selling points to attract them to a bicycle. If efficiency was high on the list of essential bicycle features there wouldn't be so many people riding round on heavy full suspension mtb's with under-inflated chunky tyres!