***[Early piper cubs had no electrical system][1]*** so an autopilot install, forgetting about certs for a minute, was simply *not possible* for a good chunk of the aircrafts history. But a lot has changed since the cubs first rolled out of [Lock Haven][2] over 80 years ago and electrical systems have been added to some aircraft. 

Its been added successfully (it seams) to some [super cubs][3] and there are lots of aircraft that now fall under the "cub" header. 

If you are talking strictly about the early J3 cubs which barely have the useful load for two modern sized adults, then adding an electrical system, servos, and the required avionics becomes a practical issue at some point. The *new* glass units that can drive autopilots make this albeit more feasible. 

I think it ultimately comes down to a limited use case and little drive for getting one certified by any major manufacturer. Most of the cub owners I know are either flying low and slow, doing aerobatics (in some cub variant), landing on river banks or mountain tops, or towing banners on clear days. These are not really autopilot-required situations as they are basically all VFR flying and some sort of special case at that. While I'm not saying you cant use an autopilot to fly VFR the real value (for the flying I do regularly) is a fully coupled IFR approach in hard IMC down to minimums, or reducing work load on a long XC flight, neither of which I really see people doing in cubs. Again this may just be the cub owners I have encountered, and with a top speed of ~83MPH in a J3 you may as well drive these days... 

The companies that sink time and money into building certified units likely also have this view and the numbers just don't drive the certification of a unit for an aircraft no one will install it in and an airframe that may not even be able to support it in the first place. 

So, urban myth, maybe, statistically unlikely, I think so. 

  [1]: https://www.avweb.com/flight-safety/technique/no-electrics-no-problem/
  [2]: https://en.wikipedia.org/wiki/Lock_Haven,_Pennsylvania
  [3]: https://www.supercub.org/forum/showthread.php?55313-Garmin-autopilot-and-Supercubs