The fascination has a lot to do with TV shows like "Wanted: Dead or Alive" 1958 which introduced the "mare's laig"; "mare's leg" was later used in "The Adventures of Briscoe County Jr.". The Briscoe County prop gun was later used by the character Zoe Washburn in the TV series "Firefly" and movie spinoff "Serenity". The TV shows and movie have a huge fan base fascinated with the gun.
J.B. Custom claims a trademark on "Mare's Leg" but lowercase "mare's leg" or "mare's laig" are generic terms. Most makers use tradenames like "Ranch Hand" or "Bounty Hunter". When Wanted Dead or Alive was on the air, a toy "Mare's Laig" was marketed, I believe by Mattel.
ADDED: "clumsy and hard to handle", I believe that was Steve McQueen's personal opinion on the mare's laig. If you want to make a replica Trapper Special short barrel rifle (12" and 14" barreled Winchesters and Marlins were sold before the 1934 NFA), getting an ATF Form 1 approved to make an SBR from a factory made mare's leg by adding a full buttstock is the easy way to go. As it is, the mare's leg is a buttless trapper.