Regardless of whether the building is concrete or wood, it will have plastic: interior decorations, exterior cladding or siding, fittings, insulation, polymerized paint on the walls and ceilings, synthetic carpeting on the floor, furniture and personal property... You won't die from spreading flames, flames spread slowly; instead, you will very quickly die from toxic smoke from burning plastic. The toxic smoke which will spread equally well in a concrete or wooden apartment building.
You can separate stairwell and elevator hall/apartment hallway with an open balcony like they do in some countries. This way smoke from the rest of the building can't get to the stairwell. This is called smokeproof enclosure.
That is most likely part of the reason why US multi-story buildings are less safe than European ones. I know that Europeans find the idea of wood frame buildings to be a little scary. Like wny do you do that?
If you look at the data, I don't think structural and framing material has much if anything to do with fire deaths. Japan also has a high proportion of wooden framing, for single family homes about the same as the U.S. This is less so for multi-story, but if you look at the numbers the fire death rate in Japan is nearly identical between single-family and multi-story dwellings. Fire death rates in Europe, even Western Europe, vary significantly across countries even with similar building practices. In the US fire death rates have dropped precipitously in the past quarter century despite continued reliance on wooden construction.
What seems to matter are other factors, such as fire warning, fire suppression, and general fire safety knowledge. But also things like electrical systems, kitchen design, cooking methods, etc.
At least in Canada, there were multiple researches on the topic and the only benefit of a timber frame is a speed and simplicity of construction. Given that they normally end up with a very similar price tag for new constructions, I don't see why consumer would prefer timber...
because the amount of firms who can build timber frame buildings is far far greater than the amount of firms who can build concrete buildings, which leads to more competition and also more housing being constructed.