Bill Tindall, E.Tn.
The original- does chromium oxide have a beneficial properly that proper selection of alumina doesn't match?

And a new one raised by Warren- will proper selection of particle size of the harder abrasives render irrelevant any friability, hardness, etc property of the softer ones. I accept that xx micron diamond will make deeper scratches than xx micron silica. That's why it removes metal vastly faster for equivalent effort. But can you achieve the effect of silica with a finer diamond abrasive? When it comes to visual appearance the answer is yes. Does a historical abrasive do anything beyond remove metal by scratching? No data revealed to suggest it does but one could make a case that it could.

BTW, add silica, hardness about 7, to your tabulation.