Crikey, you learn something new each day - I'd not heard the expression before (I live in Kent, UK and have been in the UK since I was 10) - I love learning more regional English phrases!!
My DC are 19 and 12. We are (very) lucky to live about a mile out of town, so they do a lot of walking (we all have bicycles too). During the day, there is very good bus provision between our village and town. From Yr 6, they'd walk themselves to/from school, and my youngest will walk to secondary school now (like my eldest did). Up to the point my eldest did his CBT and got himself a bike, he'd walk/take bus/cycle to where he needed to go. Some of his friends drive cars and others have motorbikes. All are responsible and sensible drivers/riders.
My DC do have to be sensible and independent with travel where possible as I'm a single parent, working FT, so I can't do school runs, lifts to work (my eldest does shift work) etc etc. I expect the DC to help out at home with chores, and (where practical) make their own way to work/school/going out with friends. I also expect them to have phones with them, to stay in touch and we all have the Life 360 app (plus the Find My Phone app).
I do say though, that if there isn't public transport, or DC1 needs a lift home and it's late at night, just to call me. In the same way, if he is out with mates and one of them is stranded and can't get home, he just needs to call me: they can come back here and stay the night, or if not too far, I can drop them home. I'd rather see that they're home safe than god knows where. This doesn't happen often though, as they do make proper plans. If they were sick and school called me/any other emergencies, I'd be there to pick them up (but that goes without saying!).
@Gettingbysomehow, that's quite scary that your DS is like that still at the age of 42! He's only a little bit younger than me!