Well even if there was a better damage model, people would still not take car of their car, only because of the instant pit ability.
With a better damage system + an impossibility of repairing instantly, then the drivers will be more cautious (especially in lap 1/turn 1 in races) as they would drive slowly in order to prevent unwated effects AND to be ready to dodge other people when in traffic.
For now, what could be done is the suggestion by Woz. Each time an object (body part or road after a jump or cone, etc), touches the engine "cube" (or tranny cube or whatever), they get a bit of damage to add up to a kind of damage gauge (the more filled the gauge is the less performant the engine or the transmission is), up to a certain extent. If a car gets his gauge full, then his car is undrivable and you get a global yellow flag for the track untill a certain amount of time, then the car autopits and the driver is not able to rejoin anymore untill the raced is finished.
So, with this, people will drive with more care, the number of accident and collision will reduce, and every body will enjoy a better driving experience