Stropping doesn't remove a burr very aggressively even when loaded. The burr folds over instead of getting cut off and thus the removal, while possible, takes a very long time.
The best way to remove a wire edge, or burr, is to cut into an abrasive at a slightly higher angle, edge first, alternating sides. You usually don't need more than 1-2 passes per side at most. The lightest pressure is optimal, so use a clean and sharp hone. You can then go back to a strop which will smooth out the transition between the main edge and the little micro-bevel you applied when cutting off the burr. This is the exact procedure you described.
A critical problem with burrs is the formation. You want to minimize this by using clean and sharp hones in the start, and you want to finish any shaping work by a couple of passes along the edge into a finer hone to cut off a burr, as coarse shaping work, especially edge trailing will leave a very large burr.
The biggest problem with burrs is that you have to use the right amount of pressure. You need to press hard enough for the abrasive to cut into the steel, but not too hard or you will fold the edge over. This is dependent on the type of abrasive, the shape of the hone, and the type of steel. For example on an Opinel on a ceramic rod I have to go almost feather light. With a 62 RC D2 blade on the same abrasive I have to press down very firmly.
It is just a matter of trial and error to determine what is best for any given knife. If you have a way to check the edge under magnification it helps as you can see the effect of the honing passes directly and not simply guess at what is happening.
-Cliff