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I believe the reason is related to the safety of the driver's position in the vehicle rather than the state of being drunk. The driver's seat is the only one guaranteed to be filled each time the car is driven, therefore car companies have a bigger incentive to care about the safety of that seat than any other seat.

People also steer themselves away so the collision is more likely to happen on the other side of the car.

They're relaxed. Tensing up in a crash means muscles don't absorb impact, they transfer it to bones and organs. A relaxed person has a better chance on a fall or crash... up to a point, of course.

Physics? I would assume the car driven by the drunk driver is travelling at a faster speed than the car hit.

s/accident/crash/g

Sorry, fixed.