I'm not into questioning safety, but growing up most people pulled heavier campers with family cars and station wagons,
I don't know what vintage cars you are referring to but the auto industry went to uni-body construction many years ago. Prior to that the cars had a full frame and were much heavier, so yes they were more suited for pulling a trailer. Today the game is to make a vehicle as light as possible, that is why we have plastic interiors, aluminum parts, thinner sheet metal and basically weaker cars. Look what ford has done this year, gone to aluminum bodies to save weight, but just wait until it gets banged up and you need someone to straighten the metal.