I use hrc, but have tried several cordages. For me the hh makes cords last longer. Not sure if it's the device itself largely being a heat sink or if the fact that on srt I am putting roughly half the 'miles' on them in general.
I bomb out all the time and have had no issues with hrc, but have had some glazing on the poly cover cords like ocean's.
I would be more worried about the high modulus fibers (technora, aramid) self abrading over time with use than wear from the friction against your climb line. You, however are the judge of your own safety and if you would feel more comfortable on a new cord then it is totally worth a couple bucks to replace it.