Melted solid wax as a filler seems like it can provide a good color match and apparently a sufficiently strong/hard surface for a lot of repairs.
Yup. And sometimes expedience is king. Because wax fillers are essentially ready to go as soon as they're set they're a very quick option, faster than any putty or other kind of 'wet' filler because there's basically no drying, setting or curing time to consider. Only shellac fillers and modern hot-melt filler sticks rival wax fillers in outright speed.
Wax fillers do vary in hardness, some are softened by body temperature and can be kneaded and pushed into place with the fingers, or just sort of swiped on like using a crayon. I think these are only suitable for the most superficial dings and perhaps not for anything that sees a lot of use. But wax fillers can be made quite hard by the addition of harder ingredients1, making the fill much more resilient, and they need to be melted into place by some means. Traditionally this was done with the soldering irons of the time, which were heated externally2. Note that modern soldering irons tend to run a little too hot for this purpose today, although some lower-powered models might work you'd want to test to be sure.
Even a hard wax filler with a high melting point might be a little too soft in service for a chip to an edge or a damaged corner, e.g. on heavy-use furniture like a table, or a piece that sees a lot of passing foot traffic like a sideboard. In this case shellac fillers might have been preferred because they're even harder (hard enough that you just score the surface with strong fingernail pressure) and perhaps more importantly they're more adhesive.
Is it a good general substitute for drying/curing wood putties?
Sort of, but where or more importantly when they're used can be different.
Wax fillers are often made specifically to be used on finished wood, to match the commonest colours seen in finished furniture woods3. Note they can be freely intermixed, and tinted with dry pigment or a dab of oil paint, to create custom shades.
Putties on the other hand are often intended to be used on bare wood, prior to the application of any stain or finish, or after just a light sealing coat (AKA a washcoat or spitcoat).
Epoxy putties are a bit of a special case as in addition to setting very hard and without shrinkage (a big issue with many fillers) they can serve as an adhesive to a degree, so are much better suited to certain types of structural repair where common cosmetic fillers would be wholly unsuitable. I think we should broadly lump together liquid epoxy that has been filled and tinted here, which is often relied on for gap-filling structural repairs so is essentially acting as filler as well as glue in those cases. And it can be thickened to any degree needed so can directly take the place of commercial epoxy putties4.
1 Traditionally by adding carnauba, candelilla, Japan or other very hard waxes to the base of beeswax and sometimes some shellac too. Separated shellac wax was also sometimes used as an additive.
2 But being careful not to use something like a candle or oil lamp as the heat source as it leaves soot on the iron which would discolour the filler. I've seen this happen, it's not pretty! Instead something that burns clean would have been used, e.g. an alcohol burners, if a brazier or wood stove were not already in the shop which could be used to keep the irons permanently hot.
3 From pale 'blond' woods (maple, ash) through the various tans (oak, beech) and browns (oak, walnut) all the way to ebony ....or these days, Java gel stain LOL.... including one or more redder tones for cherry and mahogany-like woods.
4 Because of how effective these sorts of fills are, and because they can be made to auto-fill cracks and crevices, I often wonder why pros make any use of readymade epoxy putties. And to a large extent if the user chooses filled and coloured epoxy can take the place of nearly all putties and fillers. I've used it for chip repairs to edges and corners and if good procedure is followed they're extremely hard wearing, I imagine much better than any other option except for patching in solid wood.