Of course it is.If the insulation and sheathing become too soft to resist damage if the conductor temperature is raised to 70 degC then that cable is not suitable for such use. That is not directly related to the CCC.
CCC limits for cables are not bounded by the melting point of copper, but by the behaviour of the plastics used in them (and the accessories they connect to).
That's why the It of XLPE cables is higher than that of PVC - the former can run at 90°C and can therefore carry more current.
If an XLPE cable is used in an application where it may not run at 90°C, then its CCC is reduced.
It's not a question of "if insulation & sheathing become too soft" - at too high a temperature they will , and they will, at a certain point, become so soft that the conductors will migrate through them if the cable is bent, or compressed. Keep going, and the point will come where they start to melt. Go further and they will catch fire.
But you'd still be nowhere near any CCC limit which was due to the physical properties of copper.
It's not some magic copper which gives bare 1mm² MICC an It of 26A, it's the fact that the lack of any PVC to go soft means it can run hotter than 1mm² T+E.
So yes - if a PVC cable, which uses PVC for all sorts of good reasons, which gives the cable the properties which are desirable for a flexible cable, gets too hot it becomes insufficiently able to resist the mechanical stresses to which it is subject, or at risk from, because it's a flexible cable used for portable applications. The answer to that is not to say "well if PVC becomes too soft at 70°C then it's the wrong material, and the cable isn't suitable", the answer is to limit the CCC so that it does not get to 70°C.