Back when cars were newfangled, we were completely ignorant of their hazards. We drove around with freaking plate-glass windows until safety glass was invented around 1937. Seat belts weren't even offered as an option until 1949, and no one wanted them. They weren't even required in U.S. cars until 1966.
It's unsurprising, then, that this was advertised as a good way to transport dogs by car in the 1920s:
In the 1930s, as cars became more properly enclosed and there actually was room to put a dog in the back, you still had this option: