Only HDMI 2.1 introduced link training (before that it was just the source picking a resolution that the sink supports and hoping for the best!), but even that is an end-to-end thing; the cable is not part of the conversation, so you wouldn’t know if the cable is bad or the socket/internal wiring beyond the cable on either side.
I just had to go through the "do I have any good HDMI cables" dance, and the answer was effectively no.
Fully agreed – the maximum supported data rate would be even more important to be printed on the cable for HDMI.
One reason I could see why manufacturers would be hesitant to do this is that some future improvements might not have higher requirements for cabling, so the printed data rate might be underselling actual capabilities.
The closest was one that said "High Speed HDMI cable with ethernet" but I'm not sure what "high speed" is supposed to mean