When you asked what I did in my system, I replied that I now exclusively use native HDMI for all digital interconnections between components. Absolutely not I2S over HDMI, and not any variety of S/PDIF.
S/PDIF is only designed for two channel PCM. Lack of any data error detection or correction implies that a really bad cable could definitely affect the digital transmission between your CD acting as a transport and your DAC. I have no way of guessing what the threshold of really bad is, in your system.
Equally I have no way of guessing the effects of EMI on your coaxial cable, or from your cable to other components. Note that balanced twisted pairs in theory eliminate the effects of EMI, and need no shielding. Shielding increases the capacitance of a cable, altering its analogue frequency response.
All I can say with some certainty is that your "bits are bits and are double corrected" is a false assertion in the S/PDIF context. What matters is that you are hearing differences that are real to you. Physics supplies supporting reasons for differences you hear, but not necessarily your characterisation as "smeared".
Note that HDMI uses unshielded twisted pairs for very high speed digital transmission. So do later incarnations of Ethernet from 10BASE-T on. This is why one of the HDMI pairs can be used for Ethernet.
Think about what happens when you make cables longer. Eventually they don’t work. Sometime before not working at all they will not sound good!

