How well stropping works is directly proportional to how fine an edge already is before stropping. If the apex of the edge is too thick, round or blunt, stropping won't make an improvement. That's usually a good test for determining if enough sharpening work has been done on the stones, before stropping. If the strop isn't effective at all, it's a strong clue more work is needed on the stone. And if stropping is done with fairly aggressive compounds on such a thick, round or blunt edge, the edge would more likely become even more rounded or blunt.
On the other hand, if the edge is thinned out adequately and the remaining burrs or their remnants are also as thin as they can be, then stropping on the simplest of bare materials like leather, paper, linen/denim or wood can make an immediate, noticeable improvement in sharpness.
And some steels at their typical heat-treated hardness won't necessarily burr as much as others, or hold burrs as tenaciously. So a steel that's not prone to forming or holding burrs much at all won't respond in the same ways to stropping - especially with only bare materials like leather, paper, etc. But those steels can still be refined to greater sharpness by honing them on a loaded strop using an abrasive polishing compound appropriate to the steel. In that capacity, so-called 'stropping' is more akin to enhanced sharpening and polishing by abrasion, as done with stones. But 'stropping' in its original sense is basically just about cleaning away the thin, weakened bits of steel hanging at the apex, and also sometimes about aligning a very fine, thin edge - as with a barber's straight razor for shaving.
Edited to add:
Some scrubbing sponges with a rougher scrubbing side actually use a plastic material infused with very fine abrasive particles, like aluminum oxide. Those are capable of dulling a sharp edge, if the pad contacts the edge during cleaning of kitchen knives & such. 3M's line of Scotch-Brite scourers, with green or blue rough scrubbers on one side of the sponge, are examples of those. They come with warnings not to use them on coated cookware, for example, because the abrasive in the pads is capable of stripping the coating off such items.