That's the red line in this chart: https://upload.wikimedia.org/wikipedia/commons/thumb/4/4f/US...
The period of most rapid car safety improvements came during a single ten-year period, from 1910 - 1920, where deaths, again, expressed per passenger mile, halved in only ten years.
It's not that. It's pretty tricky to get 4 wheel mechanical brakes to put even pressure on the wheels, rather than most of the force going on just one wheel. Mechanical brake linkages are fragile, susceptible to rust, dirt and jamming, and likely need constant tuning.
With hydraulic brakes, it's easy to get even pressure on all the wheels. You can even put a "bias" in that puts more pressure on the front wheels, which makes for more even and controlled braking. Maintenance is minimal, and there are a small number of (protected) moving parts.