And no, the FAA is not really that good, general aviation pilots die all the time from negligence and the FAA doesn't enforce the rules when pilots violate them (in particular low altitude flying).
That being said, the government gives general aviation pilots a fair amount of freedom once they get their license. There are rules and they are enforced; particularly when violations put the general public at risk. But there's also recognition that it's quite possible to regulate GA out of existence like a lot of other countries have, and that has pretty negative consequences in terms of pilot availability for other purposes. Therefore, regulations scale with the amount of danger the public is exposed to.
For example, ultralight aircraft (single place, <254 lbs, <=5gal fuel, <=55kts) are virtually unregulated; the idea being that they're so small and light that they aren't much danger to others. LSA/sport (1-2 place, <=1320lbs, <=120kts) are regulated; require a license and inspections but less stringent than a private license, and so on. Private licenses can't be used for commercial purposes, and generally speaking more training and endorsements or ratings are required for eg. aircraft with multiple engines; those that are >=12,500 lbs, those that land on water, those that have old-school landing gear, etc. etc.
§ 91.119 Minimum safe altitudes: General.
Except when necessary for takeoff or landing, no person may operate an aircraft below the following altitudes:
(a)Anywhere. An altitude allowing, if a power unit fails, an emergency landing without undue hazard to persons or property on the surface.
(b)Over congested areas. Over any congested area of a city, town, or settlement, or over any open air assembly of persons, an altitude of 1,000 feet above the highest obstacle within a horizontal radius of 2,000 feet of the aircraft.
(c)Over other than congested areas. An altitude of 500 feet above the surface, except over open water or sparsely populated areas. In those cases, the aircraft may not be operated closer than 500 feet to any person, vessel, vehicle, or structure.
(d)Helicopters, powered parachutes, and weight-shift-control aircraft. If the operation is conducted without hazard to persons or property on the surface -
(1) A helicopter may be operated at less than the minimums prescribed in paragraph (b) or (c) of this section, provided each person operating the helicopter complies with any routes or altitudes specifically prescribed for helicopters by the FAA; and
(2) A powered parachute or weight-shift-control aircraft may be operated at less than the minimums prescribed in paragraph (c) of this section.
Except when necessary for takeoff or landing, no person may operate an aircraft below the following altitudes:
(a) Anywhere. An altitude allowing, if a power unit fails, an emergency landing without undue hazard to persons or property on the surface.
