Well, that certainly sounds safe. The old fashioned fabric insulated wire was usually rubberized as well, but you only see the rubberization if you cut through it. This was OK for the period, but tended to wear out and fray relatively quickly, plus suffer more rodent and insect damage than modern insulator materials, and, since it was often cotton, it could even decompose due to mold in damp climates. Overall it’s a much bigger fire hazard than modern wiring. One “solution” in the 40s through 60s to these problems was to make the cloth insulation from woven asbestos, but that just trades one safety problem for another. Really the issue with polymers is that we’ve gotten so inventive with them that nature doesn’t have good ways to safely decompose them. The natural world is full of polymers which do break down in non-problematic ways, like wood, so really the right response is to learn from that and engineer plastics which have long service life, but a “graceful” and biocompatible decay process. There’s been some work in this area, and not all plastics are equally bad. It’s a good idea to avoid using them where it can be avoided, but other good solutions include using less hazardous ones.