IMO, the original rationale for a sidearm and longarm chambered for the same cartridge contained both practical and economic factors.
When Winchester introduced the 1873 rifle and carbine and the .44-40 cartridge it represented the most practical all-around compromise of power and magazine capacity available. Colt revolvers were offered a couple of years later, with other manufacturers not far behind. The subsequent marking of Colt SAAs so chambered as the "Frontier Sixshooter" pretty much says it all.
On that frontier, the relatively new self-contained metallic cartridges were expensive, and resupply could be difficult. Obviously, having the advantage of only having to buy one cartridge that would give a person performance levels adequate for his most urgent needs in both his sidearm and longarm was a most practical option.
The .44-40 might not be the absolute 'best' for a particular situation, but it would sure do well enough in almost any situation to get you fed or home with your scalp intact.
With blackpowder, there was and is a much more marked ballistic gain when fired from a closed breech and through a longer barrel. That, along with the increase in both precision and effective range most folks obtain with a longarm made for a 'slam dunk' choice where your resources were going to be severely limited.
For the shooter of both limited means and interests, a carbine and sidearm chambered for a "Magnum" revolver cartridge still has great practical value, and for many of the same reasons.
Modern semi-auto pistol cartridges, as has been noted, just don't offer nearly the same level of ballistic gain from a longer barrel to extend one's effective range to as significant a degree. For the indifferent marksman, there may well be a significant gain in precision, but without a commensurate increase in energy delivery.
I would argue that the combination of a .357, .41, or .44 Magnum carbine with a revolver of the same chambering can cover more bases better, in more conceivable situations, for more people than the same combo in any semiauto pistol cartridge with the possible exception of full-power 10mm Auto rounds.
IMO, the relative lack of practical advantages to the system when semiauto cartridges are used is the main reason that sales of carbines so chambered are relatively small when compared LAs in Magnum revolver calibers, even in cases when prices are directly comparable.
It's not just nostalgia; it's something that works better.
