I think the validity in cold testing lies in suspicion of engine damage, thus engine should not be run until compression is confirmed.
Same thing is true for an engine coming out of deep storage. We oil them up well before initial cranking and compression testing to determine condition, and in the case of a good condition running motor, proceed with bench running prior to installation.
For example, in the case we receive a remanufactured replacement engine for install in a customer's mercruiser, we always run-test that engine prior to installation.
I think it's important to note in that case we don't perform pre-startup cold compression testing in order to avoid wiping assembly lube off the crankshaft journals and camshaft lobes. Instead, we prepare it for a quick startup by making sure the system is fully functional prior to first crank.
So a blanket statement just doesn't apply, the compression test parameters and sequence vary depending on circumstances.