Asian here. Never took public transit until I was in my teens. And I wasn't alone - I don't remember a single kid from my school who used public transport when they were less than 10yrs old.
Well Asia is literally the biggest continent on earth with a population of over 4.5 billion people so some mileage may vary. I don't expect growing up in Tokyo is all that similar to growing up in rural Turkey.
I grew up in a west Asian country and walked to school every days from age 6 to 18. I didn't get on public transit on my own till probably my teens either because I didn't need to!
Everywhere I needed to get to was within walking distance. I sometimes walked for an hour to get to my sister's place on the other side of town but my schools were first 5 minutes walk and then 15 minutes walk away from where my parents lived.
It's very normal in Korea, Taiwan, and Japan. Once kids are out of kindergarten, it's assumed that they're able to get from point A to point B without much help.
So I don't know which Asia you are talking about.