It is a false idea that the earlier cars were safer.
Most of the older cars were still not much more than the Model A. Some fenders hung on a body bolted to a frame. It was all decorative. The bodies ability to protect the people was limited. There was little if any thought in how to use the structures to absorb and transmit crash energy around the occupants.
The cars survived more on just pure 'mass' it was big metal and ordinary collisions at low speed (most accidents are around town low speed) would not be able to move very far into the metal. For higher speed (higher energy) accidents the cars collapsed and tore apart quickly. It is scary to look at all these 'safe' big old cars in the coffee table book full of accident pictures. They all came apart at any real speed.
Here is an example. Notice how the fender of the 59 is effectively useless and just tears away. You can see that the firewall of the 59 was crushed in, not good for someone in the drivers seat.
59 vs 09 Impala
The modern cars are 'glued' together and have strategically placed crumple zones to allow for the energy to be absorbed outside the passenger compartment. Well I should say in places to minimize occupant damage cause some cars are just too small these days.
With the advent of seat belt usage and other safety features the severity of injuries and death rate in modern accidents is way down. The cost is what you see in the basically disposable cars we see today.