Those decades were an era that followed massive airline deregulation. This is another case of the good regulation being less regulation.
If the FAA were to disappear tomorrow, I guarantee with absolute, utter certainty, that aviation's safety performance would drop--in some cases over time, in some cases, overnight. I would bet any amount of money on that.
To wit, three prominent examples of industries frontrunning safety advances well in advance of any regulation around them. One: In the late 19th century, early electrification was burning cities down. Private insurance companies banded together to form the Underwriter's Laboratory to test products, refusing to insure buildings that didn't use UL-listed devices. Manufacturers voluntarily submitted to rigorous safety testing not because the police would arrest them, but because it got them access to insurance at a considerably lower cost.
Two: In 1959, Volvo engineer Nils Bohlin invented the three-point seatbelt. Volvo gave the patent away voluntarily to all competitors, partly to establish a brand identity of safety and innovation, and partly because they genuinely recognized that seatbelts saved lives. If your claims were right, Volvo would have either kept the patent to monopolize safety or, worse, buried it to save manufacturing costs. Instead, the market rewarded them for being the "safe car," and other manufacturers had to follow suit to compete, decades before seatbelt laws became universal.
Three: There currently exists almost no federal law governing recreational scuba diving in the United States. Yet, the industry is obsessed with safety. Shops by and large will not fill your tank without a C-card. The PADI and the NAUI update their standards constantly. If tourists started drowning en masse, in a sport virtually custom designed to do so, the industry would vanish. They self-regulate to preserve their market cap.
With all that, let's return to the claim you are endorsing. You say you are "absolutely confident", >99.99%, that the FAA's dissolution would lead an entire industry to be less safe a century from now. This seems like, at minimum, a lack of imagination regarding how markets solve coordination problems. You are assuming that in the absence of the FAA, a vacuum would remain. History suggests the opposite. Indeed, it seems entirely possible that without a shield of regulatory compliance to hide behind in court, liability pressures might actually make airlines more risk-averse, not less.
It is "irrational" for a "greedy" slaveowner to kill their slave, a significant monetary investment sometimes, and yet it happened all the time, because capital owners are not rational.
A significant fraction of aviation fatalities can be traced directly back to those "greedy capitalist villains" actually completely cutting corners to save a penny and losing million dollar aircraft.
Business owners are not rational actors, they are gamblers.
For example, you say lawsuits are costly. To a company, that's meaningless. The only question is, is the cost of a lawsuit greater than the money saved cutting corners? If not, it's better to kill people and deal with the lawsuits: [1].
Moreover, companies are still run by people, and people have biases. Most notable of which is the short-term thinking bias that results in companies irrationally optimizing for short-term gains, compromising long-term ones. And what fits perfectly into that trap? Yep, safety. Do you know how much money you could save by delaying maintenance? Lots, lots of money to be had right now vs a nebulous concept of potentially higher chance of an accident at some uncertain point in the future. The monkey with its primitive brain chooses the immediate reward every time.
You probably meant public companies because otherwise this sentence and rest of your comment do not reflect reality.
According to [0] (2019), 90% of (6.1m) businesses have < 10 employees. Lawsuits are a very big deal to these enterprises. They are not out to kill people for marginal profits.