Cars won because they were (and are) better than the alternatives. The need for powerful individual transportation with utility has always existed, and was originally met with horses. Bicycles meet the transportation need, but not the need for utility. Cars do both, and they do it better than anything else. Even before fueling infrastructure was rolled out, you could still run a car on petroleum you bought from the chemist, which is still infinitely better than the acres of pasture you need for horses. If you had an early diesel, it would run on oil, which is even easier.
The idea that cars needed all this infrastructure that other alternatives didn't just doesn't match the reality of the history of the automobile. And yes, we've leaned on those advantages in the century since, which has also created vast areas where a car is necessary to participate in society, but we only did so because the advantages and utility were so undeniable.