Burn in is measureable with speakers, it has been found in woofers in cars and cinemas (I am not aware of a purely audiophile test). What was also found is that if a speak rests and is not used for a few days, it returns to its original measurements. So the burn in process is not fixed and it varies as to the regularity of the speakers use. But how audible that burn is, is not clear. Then no connection between the change and sound quality has been shown.
To show that burn in exists with a cable you need to 'A' measure and show a change, 'B' show it is audible and 'C' show it affects SQ. So far no cable maker has done that, nor anyone else. One should ask oneself as to why that is. Why has no cable maker or anyone else who claims burn in stepped up with evidence of 'A', 'B' or 'C'?
Claims of I heard a SQ improvement with time so 'A', 'B' and 'C' must occur with burn in is appalling science and should rightly be held suspect and questioned.