score:20
Most airlines set a minimum age where children can travel alone. The exact policies will vary between airlines, but they generally work like this:
Minimum age to fly alone at all. This is often around age 5 for airlines in the US. Children below this age must always fly with a parent or other responsible adult.
Unaccompanied minor service. Some airlines offer this service for an additional fee. It is often required for children age 5-11 or so and optional for kids 12+, but the rules and age cut-offs vary between airlines, with some requiring it through age 14 or even 15. The airlines will also set rules about when this service can be used: some won't offer it on international flights, or itineraries with any connections, or itineraries with tight connections, etc...
With this service, an adult must bring the minor to the airport, get them checked in and signed in with the airline, and airline staff will escort them from place to place as needed until they arrive at the destination and an authorized adult shows ID and picks up the child. On board, the flight attendants will introduce themselves to the unaccompanied minor and will give them some extra attention, though kids are still generally on their own during the flight and should be able to occupy themselves. If there are connections, airline staff will escort the child to their next flight. In many cases, the adult dropping off the child must wait at the airport until the departing flight has taken off as well.
No supervision required. Above this age (somewhere between 12-15 for many airlines), the airline's policy does not require any supervision. Some airlines may still offer optional unaccompanied minor service for older travelers if parents want to pay for it. Parents should still consider their child's maturity and their ability to solve problems or get help if things go wrong.
As always, parents need to know their kids best and decide what is appropriate for them. Many five-year-olds may not be ready to fly by themselves, especially if they've never been on an airplane before. Some 12-year-olds may be seasoned world travelers and not need any assistance. Ultimately, parents need to decide this for their kids before making travel plans. There's a big difference between a direct one-hour domestic flight and a three-stop 24-hour around-the-world trip.
The exact policies and even the availability of these services will vary from airline-to-airline (and many low-cost-carriers do not offer unaccompanied minor service), so it's important to research all possible airlines and the fees involved before booking tickets. Most airlines have a page on their website explaining the policy, and a search for the name of the airline and "minors" will bring it up.
I certainly wouldn't say that it is "extremely dangerous" for kids to travel alone. As with all travel, there's a risk that things can go wrong due to delays, missed connections, bad weather, etc... The result is generally lost time and inconvenience, which may certainly be stressful for kids, but isn't "extreme danger." All the requirements for human life, telephones to call home, airline staff who look after unaccompanied minors, etc... are all available at airports.