Just to give an idea where I'm from:
* in my home country (one of the highest GDP/capita, so we're not talking poor&rural), children are walking alone or in unaccompanied groups to kindergarden at age 5-6. if parents try and drive them they're often scolded by school authorities, they're supposed to handle it by themselves.
* in Japan (just another example that I know well), children walk to school at age 5-6, accompanied by a 1-3 year older sempai that explicitely takes over the responsibility for younger colleagues. There's also people taking the responsibility for a given street corner at a defined time in the morning, watching out for the youngins a bit (but it's not necessarily their own). Again, people who drive their own are typically scolded by society.
* after school, children in both countries typically go do other activities on their own, like go to football club or in case of Japan do some school club activity. Curfew time is typically before dark or around 5-6pm.
* from time to time there tends to be an accident or case of violence/murder against children that might have been avoided without this culture of letting them run. people are outraged against the person who did it, but culture of self responsibility is not questioned and life goes on. risk is typically 1/1 million or lower (relatively safe drivers, low levels of violence).
No one is scared to let their children out because of violence or murder. That’s silly news media fear mongering unless you live in a bad area.
How close is the kindergarten to your house?