Lately I've been going to the strop after the soft Arkansas stone for most applications, with the intent of ending up with a bit of polish on a toothier edge. If the steel is hard enough and the sharpening technique good enough one can forgo the strop, the Dozier factory edge being a good example of an agressive, toothy edge that still cuts hair on one's arm. I'll guess that for most people the strop effectively 'hides' less than optimum technique using a stone, it certainly does for me, as it is difficult to consistently work an edge with increasingly smoother stones without increasing the sharpening angle. It's also difficult to get a lot of edges straight enough to be able to use on wider, smoother stones, where again the compliance of the strop helps to overcome the problem.
I find that with the typical gummier, softer stainless steels it's better to go to a finer stone before stropping, or to just finish off with a fine stone or ceramic stick. I'll guess it's because the wire edge is gummier with the softer stainless and doesn't respond as well to stropping, and is also why the Spyderco sharpeners are so popular.