It's from the UK but it's probably even worse in the US (I think in the US now most kids aren't allowed out of the yard of their house on their own until they're old enough to drive basically.)
I can't figure out what it is doing this - I'm UK-based too, and I know logically that everything is now safer - I used to walk two miles to the woods with friends at the age of eight or nine, but I wouldn't trust my own children to walk to the bottom of the hill here.
I don't really understand what has changed. Why were my own parents less paranoid? There are lots of people giving lots of reasons on here. The most credible is the constant "stranger danger" message pumped out in news, but I honestly wonder if there's been a baseline increase in people's general paranoia - my concerns are more around them doing something stupid and getting into trouble.
The UK in particular is somewhat obsessed with "health and safety", which is probably #2 on the favourite thing to complain about (after the weather, of course) but at the same time people gleefully participate in it too.
I lived in England for a while (as a Dutch person) and my English girlfriend was always paranoid about things I didn't see as a problem, for example I was perfectly comfterable carrying stuff from the car to the house and leaving the car unattended on the (enclosed!) parking lot for a minute, but she'd insist on locking it. N=1 of course, but I observed a number of other similar things over the years I lived there with different people. When it snowed for a bit the British were in a state of near-panic, and things like the Met announcing "there may be power cuts and shortages" didn't exactly help calm fears. It's 5cm of snow people, announced a week beforehand. We don't get snow that often in NL either, but I've never seen it anywhere near as chaotic as in England.
I guess I'm rambling a bit here, but my point is I think the problem is wider than just "kids". Partly, I think that's good: we're more aware of risks and deal with them a bit more consciously, but you can go too far in this; a risk-free life is a boring life hardly worth living.
"It's dangerous" or "it's a risk that [..] will happen" is almost always true in a sense and hard to argue against; "yes but no life can be without risk" comes of as weak, especially when it concerns something like your children.
But like you, I don't think I'd be happy with my kids doing things like that (my kids aren't quite old enough yet anyway).
I think part of it is realising that some of the things I did were pretty fucking stupid, and could have ended very badly. For example, I recall exploring a dilapidated house that was falling to pieces - in the middle of nowhere in rural Scotland. I could very easily have died if something had gone wrong.
I'm certain the media is a large part of it too - the overwhelming focus on doom and gloom feels very unhealthy for society as a whole.
That doesn't explain all of it though; I realise we live in safe times, but still find myself being overprotective, sometimes seemingly irrationally.