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Maybe bigger cars are safer if they hit walls, but it's not entirely obvious to me. The more massive the car, the faster it will still be going when its front crumple zone finishes crumpling and wall and windscreen make contact; isn't that bad? Slower driver deceleration isn't a good thing if the still-fast-moving driver starts colliding with bricks.
Anyway, most car accidents don't involve hitting walls, and many car accidents endanger people other than the occupants of the cars, which means more mass => more danger.
A more massive car has more energy to dissipate but also more structure (crumple zones) to apply this energy to. The net balance is not obvious me, either.
While most car accidents do not involve hitting walls, a lot involve hitting objects-other-than-cars (guard railings, trees, animals, etc.) where being heavy can be an advantage (because that excess energy that you have you dissipate into the object). As to pedestrians, the mass discrepancy is big enough to not matter -- the consequences to the pedestrian of being hit by a 1-tonne car are the same as being hit by a 2-tonne car.