One of the things that is different about power cords vs ICs and speaker cables is there is always voltage present as long as power is supplied whether or not the device is turned on. If the dielectric is the primary thing that burns in, it seems to me it is the capacitive property of the cable that is affected and current shouldn't matter. What say ye?
It is considered that some of the long time period it takes for some particular cables to burn in is the 'burn in' of Teflon dielectrics.
Some cables might be 100 hrs and some might be 500 hrs. the 500hr burn in ones , when looked at closely, tend to show up as having Teflon dielectrics involved in their construction.
This is where cable heaters will generally try to deconstruct or shut down any potential avenue for this to be assessed, or discussed at all.. via trying to find a single cable that calls for a long 'burn in period' where that single example has no Teflon (from their reading) involved... and then bring that up as some sort of black & white simple man's, blinkered in origin - occam's dragon slayer. Please. Stop. Just stop.
There are some good discussions about Teflon dielectrics in these cable scenarios, but one will have to search around for it.