david weaver
The comparison being made here is a small edge from a tool vs. polishing a large surface. The latter is an operation with an easily measurable economic component, but I don't think the increase in speed for very tiny abrasives is that relevant the way most people are using chrome ox on edge tools.

I've got abrasives down to .09 micron (iron oxide in that case), and have diamonds (which I've lost) down to 0.1 microns (I can't recall if I ever actually used those - I used the iron oxide on razors). Even fresh iron oxide will blacken quickly. The edge on a razor from the iron ox is noticeably improved very quickly, but it is in the stratosphere for sharpness and it will cut the hair and any skin raised behind the stem of the hair without noticing (that leaves nasty razorburn).

That aside, there is one advantage to chrome ox that wouldn't see me changing to alumina, well, two:
1) the only place I really use anything like that is razors. The gentleness is appreciated - I was probably need to go to smaller alumina to get the same feel and the speed difference would be negated
2) most importantly - the visual clue about how much compound is on a surface at any given time is always there with chrome ox because the compound isn't tinted leaving behind an ink, the color is the actual abrasive. That visual aspect is nice.

There's a supplier of lapidary products here in pittsburgh, but it's far enough away from me that making a drive it for one or two things would negate any savings. And, as you say, they generally have sample or giant. Not much in between. as i recall, they had alumina as small as .05 micron. If I buy a $12 pound sample of alumina, then I have it to deal with, I've lost the color reference, and tax and shipping are another $12. A drive to the place and back (which goes right through the middle of the city) would take an hour or an hour and a half, even though it's close. And it would solve a problem that I don't have (which is that the refinement of the edge should leave said edge ready for the next step. An oilstone edge that's completed properly is easily finished by chrome ox.)