Stepping back from the OP’s question of specifically DSP, I think there’s more to this. The issue really is that most listeners (queue the "not me" trolls) are most sensitive to frequency response variations. In this sense cables are on the low end of items that can cause these variations.
Speakers, room placement, tone controls, DSP, room treatment or lack of. All of these have the potential for very large variations in frequency response. How bad? Well I once measured a subwoofer with over 20 dB peaks and dips in the in-room response. That’s a factor of something like 20x more power at some notes!!
I see a lot of evidence of listeners being tricked by ragged mid/tweeter responses into believing they are hearing more detail, who don't realize what they are hearing is just a different tonal spectrum. I also know some listeners can go to an audio show in terrible sounding rooms and seemingly ignore the room’s acoustics. So this rule isn’t always true, but I do feel, strongly, if you are training your brain’s neural net to hear speaker cables but not the room your perception is now heavily unbalanced.