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Heavier cars are safer for the people in the heavier cars, and more dangerous for others with whom they may collide.
This produces a sort of evolutionary arms race in the direction of larger heavier cars, making everyone less safe overall.
(Other changes in car design have made them much safer over the years. Today's cars are much safer than those of, say, 30 years ago. But not, I think, because they are heavier.)
While at first I thought to agree with you, I have a counterexample. Bigger car is safer if it collides with a wall, small ones and bikes are more dangerous in this case, because they result in quicker deceleration of the driver.
So longer cars are also safer, and longer car tends to be heavy ones. So if all cars will be large we will get safer driving environment.
So it is easy to imagine "absolutely" safe car: it would be large, heavy and very slow (like 30 miles per hour).