Because yeah, I agree with you that in that sense cities are better than the often car-centric countryside for teenagers; but for young kids (elementary school and below, which is what the article covers) it's a very different equation.
After school they're getting themselves home as well, often in groups causing the traditional nuisance in newsagents and supermarkets (thank god the energy drinks are now not sold to kids!), and going to parks and whatever.
I think they have to be a little older to confidently get their way into Zone 1 on their own if they should need to, but I regularly see youngsters I'd guess are 11-12 years old going into town on their own, clearly to meet friends.
Despite what the media (and for crying out loud, the US President), says, London is actually a remarkably safe city. Murder/homicides are at a low they haven't been at for decades (possibly centuries), and while sexual assaults are rising, that is seen as mostly attributable to more reporting (victims coming forward more). In the case of assault on a child, that's more likely to occur in a family setting than it is in a public place during daylight hours.
I'm not sure what the media or president is saying, but looking at the data I would not call it "remarkably safe". It sounds like the London violent crime rate is 28 per 1000 while New York and Los Angeles are about 700 per 100,000. I wouldn't let my kids ride public transport all over those cities until they were at least teens (the laws might not allow it anyways).
I guess it's possible they're small but not <12yo
In some countries and even US states this is already an age you can marry.
They were never on the tube with me, but plenty of children would be arriving at about 8:15, as I was departing to get to work for 9:00. Private school children are more likely to have a longer journey to school, therefore less likely to have a direct bus, and presumably more likely to have parents who will pay for the tube/train. (Only buses are free for children.)