Prior to cars walking anywhere in any street was completely normal. You can watch movies filmed before the 1920s and city streets are full of people walking around or congregating.

If a wagon or trolley hit someone that was considered the fault of the driver, every time.

When cars started arriving and being driven around by people who were wreckless and bad at it, you started getting manufacturers and "motorists" lobbying for the concept and laws around jay-walking. Even the word was a way to delegitimize what used to be normal. "Jay" was negative slang for country-person (think red-neck). The idea was "modern city people stay out of the streets!"