I don't bother with a strop. My axes tend be fairly soft steel and do rough work so, as noted by others, I don't see a lot of value added.
That said, a firm power buffing wheel with polishing compound might add value on cheap axes, because you can harden the edge very slightly if you want to. Barbarous, but effective.
For a really high end axe like Wetterlings or whatever, the steel quality is good enough to make stropping worthwhile. But they're spendy -- I would be scared to take it out of the vault.
