I have no technical knowledge but can imagine the potential difficulty finding the ideal synthetic leather, that will perform well in all temperatures, from +50c (or more) to minus 50c. Something real leather does much better.

Thin,more pliable, synthetic may perform better than thick 'tough' synthetic leather where maybe the extra thickness of the pvc layer makes it more susceptible to stress cracking.
I agree this is made worse on the Jazz because of the way the material is stretched under tension behind sharp edged hard plastic side panels.
So I do not fully condemn Honda when the passage of time in real world usage, reveals a weakness that was not picked up during mechanical tests in a laboratory.
Honda's fault lies in their attitude to resolving the issue. They should, without question, rectify it under warranty, or as cars go out of warranty, and fair wear and tear might become a reasonable explanation , Honda should make available, at a reduced price ,or even free , a repair panel solution designed for easy DIY fitting.
Few cars these days use real leather. Its unacceptable to many buyers , not only vegans, or those who will object to the use a particular species of animal for religious reasons.
Also unacceptable is Hondas apparent continued use of the word 'leather' in advertising to describe the material. Maybe the reason is when information is translated from japanese original into various local languages insufficient care is taken to ensure it completely accurate.