I don't believe the Walkers, or the subsequent Dragoons, were primarily designed as "belt guns." They were true horse pistols, carried in scabbards on either side of the saddle's pommel. Again going on memory, I think the over design, and over powering, of the Walker was quickly recognized. The Dragoon wasn't much lighter but it was somewhat shorter and the powder charge was reduced. Clearly, the better balance in a .44 was eventually achieved in the 1860 Army.

Regardless of how often these guns show up in stories they were very expensive and there weren't all that many built and it took a LONG time for them to filter out onto the civilian market. The movies, which like a lot of shooting, tend to pretend that new revolvers and then cartridge pistols were common. This is probably inaccurate. Dad knew guys in the 1920s who still carried cap and ball revolvers for protection. It was what they could afford ... very similar to someone carrying a 1950s era revolver today.