Roman Landes has done research on this. His book is Messerklingen und Stahl. He is a regular in hypefreeblade.com ( a metallurgical knife site). Cooling from black heat and from temper has been discussed there a good bit.
I think Verhoeven discussed it, too.
From black heat, quicker cooling rate avoids the formation of fine pearlite. From temper, it makes any RA drop toward the Mf more rapidly, and not stay stabilized as austenite.
This is a metallurgical reason more than a real world problem. The difference is detected in a lab by metallurgists who care about things like %RA, but you couldn't tell one blade from the other in the field.