Smokeless powder produces much higher pressure, weight for weight, than black powder. Nuff sed. Further, the pressure curve for smokeless is sharper than for black powder; in other words, the blow is not only harder, but faster, and that is what blows up old guns.
Could those conversion cylinders be used with lightly loaded .38 Special? Sure, but if the maker says .38 Special is OK, people will stuff in the hottest load they can find and the gun won't take it.
.38 Long Colt was never loaded to a high pressure level and so by saying that the cylinder is OK for that round, they avoid the problem of hot .38 Specials.
The design of the gun itself is involved, too. In a percussion revolver, recoil drives the whole cylinder back, putting pressure on the center of the standing breech, where the frame is thickest. In a modern revolver, the case pushes back against the upper part of the breech, and the extra leverage trys to bend the breech back, straining the right angle at the lower rear of the cylinder window. That is compensated for by the top strap, which keeps the gun together.
But when you have a conversion cylinder in a Colt-type percussion gun, the strain on the breech is like that of a cartridge revolver, but without the top strap, so the gun is inherently weaker than a modern revolver. In addition, many percussion revolvers are made with brass frames, which are also weaker than steel frames.
In short, even if the conversion cylinder will take .38 Special, assume the makers know what they are doing, and do not use loads exceeding the pressures of the old .38 Colt.
Jim