To me, this THD/SINAD discussion is "history repeats itself" type. In the 70's first Tapio Köykkä was building circlotron-type(*) tube amps and complained that new transistor amps with extremely low THD sounded bad and distorted transients. And everybody was like, it cannot sound bad, the THD is absolutely minimal, here are the measurements! Until Technical Research Centre of Finland did some research on this, and Leinonen, Otala & Curl published a paper how to measure this type of transient distortion. Later also came so called Otala & Lohstroh amplifier that fixed these issues (Harman/Kardon and Electrocompaniet productized this).
So overall, IMO, there's no single measurement that exhaustively describes performance, but instead it is very complex matter with multiple aspects.
I've started using TIM measurement for DACs too. Here's just one:
View attachment 34799
The four high peaks are part of the test tone. Rest of the lower level peaks shouldn't be there.
*) At the moment Yamaha A-S2000 -series amps are using MOS-FET based circlotron circuit, but I don't know of other commercial implementations at the moment.