I disagree, somewhat. If the hole is tapered, it would be a friction fit, just like some chucks fit a tapered arbor on the smaller drill presses.
Using these wrenches, the tapered shank of the calk would be turned to pop it out of the tapered hole, particularly when they wear down.
Ever accidently bind up one of the taper fit chucks on a drill press, and have it pop off? I have. They pop right off.
Hot shoes wouldn't be on the horse. These calks were made to be applied when needed, for traction. Or removed easily, by popping them off the shoe while still on the horse, easily done with a quick twist of the wrench. The hammer face looking side would be used to tap them into place.
Also, looking at issues of the Blacksmith and Wheelwright magazine, you will find many companies made the shoes ready to accept the calks, with the holes made into the shoe. Different companies claimed they had the best calks, "guaranteed not to fall out".