Even though a 19th century design, they are not used in the Single Action Shooting Society for some reason.
Howdy
Did you not understand the name Single Action Shooting Society? We shoot Single Action Revolvers in CAS. Not double action. There are lots of 19th Century revolvers that are not approved for CAS competition. For instance my S&W 44 Double Action Top Breaks. Not approved because they are not single action revolvers. I have been allowed to shoot them a couple of times in local matches as long as I only fired them single action, but absolutely not allowed in major competition, no matter how they are fired.
Actually, the whole replica single action revolver industry started long before anybody had thought up Cowboy Action Shooting. CAS did not start up until the mid 1980s.
Val Forgett II worked with Uberti back around 1959 or so to produce the first of the replica single actions, the Colt 1851 Navy Cap & Ball revolver. The centennial of the start of the Civil War was approaching and Val correctly guessed there would be a lot of interest in replica Cap & Ball revolvers from that period. Val started Navy Arms about that time, the first major importer of replica revolvers, taking the name from the Colt Navy revolver. I'm not sure exactly when Uberti started making replicas of the rest of the Colt Cap & Ball revolvers, or when they started making cartridge single action revolvers, but it all started around 1959 with the 1851 Colt Navy. Ever since there has been a steady demand for replica single action revolvers.
In fact, membership and participation in CAS peaked a few years ago, and has been declining a bit recently. But there are still lots of replica single action revolvers being made and sold. Far more than there are CAS shooters. A lot more people than just CAS shooters are buying replica single action revolvers today, the demand is still high.
Regarding the 1892 Colt, besides not being a very good design, there simply is no demand for it. That's why nobody is making a replica of it.