IMHO, the Walker and the subsequent Dragoon models were designed to be what used to be referred to as "horse pistols". IIRC, they were usually issued in pairs and carried in a holster rig intended to be slung across the pommel of a saddle. Their role was to provide the 'heavy' cavalry troops of the day (Dragoons) with a versatile and effective replacement for the single-shot percussion carbine.
The role of Dragoons especially, and cavalry in general, in the tactical order was changing fast. Formerly, Dragoon units would usually ride into battle but end up doing the majority of their fighting dismounted, infantry fashion. The advent of a reliable, powerfull repeating firearm (the Walker revolver) enabled them to be much more effectively utilized in a "shock-and-awe" type role where full advantage could be taken of their speed and mobility.
Also just MO, but I believe that the design of the 1860 reflected another rather significant paradigm shift, as it was obviously intended to provide roughly-comparable power in a package which could be routinely carried on one's person. Try doing that with one Walker or Dragoon for a while, much less a pair of them!
P.S.: Every time I rewatch "Lonesome Dove", I always wonder how Gus managed to keep his pants up with 4 1/2# of Walker hanging on his hip.