@DaydreamzThere's a broader point here - it's not just the age at which you can leave a child alone unsupervised (which obviously varies by jurisdiction), but - as many people have noted - the shifting attitudes of society and parents.
The key is really risk-averse policies. This:
A child age 7 and under cannot be left alone at home for any period of the time. This also includes leaving the child unattended in the car, backyard, or playground.
isn't really about the welfare of the average child. I suspect every single person that I know who was a child in the 1960s and 1970s was left alone to play in the backyard at ages under 7. My kids played by themselves that way in the 2000s, for that matter, but we were unusual parents by that point, perhaps.
Somewhere between 7 and 9 I started routinely walking to elementary school by myself (about a 15-20 minute walk, crossing one major street - with no light or crosswalk - and several minor streets). No one thought that was odd or unsafe.
When on road trips I routinely laid down in the back seat (no seatbelt) and read. I can't read sitting up in a car due to motion sickness, but lying down, book held up, worked just fine.
Whether these things are "safe" depends on what you mean by "safe". If 100,000 children are allowed to do them, a few will be seriously injured or die. That will happen. A kid walking to school will be hit by a car, a kid playing unsupervised in the backyard will fall out of a tree or off the roof or antagonize the wrong snake or whatever, and the kid without a seat belt will be killed in an accident.
We are risk-averse and "death or serious injury" is an easy standard. Who wants their child dying or being seriously injured, right? So we put an ever-growing web of custom and regulation in place to preclude behaviors that have a measurable risk of problems.
The thing is, as a society we're lousy at measuring the long-term cost of these things. There was an article long, long ago (late 1990s, I think), in which someone said, "The number of children admitted to ERs with broken bones from falling out of trees is at an all-time low. This is a bad thing." The point was that we're putting so many guardrails on life that children aren't given a chance to learn how to assess and manage risk themselves, so they do incredibly stupid things once they're on their own. Obviously, if it wasn't safe, someone would've stopped them, right?
For the story, I'd say sixteen or the like is entirely plausible given the parents you're describing (as long as this is a parenting issue and not a police/CPS-response issue).
It depends on how you write the child, though. "Unruly" and "throws a party" doesn't mean "incompetent". My kids could've managed just fine at sixteen. They also quite possibly would've thrown a party and trashed the house. But many of their friends would've been utterly lost at sixteen.
My kids could cook (unsupervised) simple meals (grilled cheese, scrambled eggs, etc) at ten or so. Some of their friends can't cook at twenty.