Before there was technology for power generation and distribution at scale, "you can use electricity to make light" was a mere curio. Fit to be showcased at fairs, but not something that could be put to practical use.

The first arc lights were made in early 19th century - not long after the invention of voltaic pile made electric power readily obtainable in a lab. But it wasn't until late 19th century that arc lights began to be used as street lights. Why?

Because dynamos and alternators didn't exist in early 19th century. They only became usable for industrial power generation in the late 19th century.

Only when both power generators and arc lights were viable, electric lighting became practical. And electric lighting becoming practical has, in turn, caused electric power to be deployed at an ever-increasing scales, and spurned further investment into electric light, generators and transmission line technology. The invention of incandecent lights fit for household use and the war of the currents were both downstream from better power generation technology.