I'm not one to defend the public education system, which makes this feel strange: they aren't the result of a failed educational system at all.
If that is your measure for failure, then no hypothetical education system could ever hope to succeed, no matter how well-funded or well-regarded, no matter which genius experts you put in charge of it, no matter what philosophy it operates under.
Humans number in the billions. When there are billions of them (indeed, a large fraction of a billion in the United States, where I believe the flat-earthers are the most prominent), it is inevitable that some tiny percentage harbor contrarian and anti-authoritarian personalities of the sort and degree that will gravitate to nonsense like this. They cannot be educated out of it, indeed, education may actually backfire as they learn just enough logic to misapply it to science and dream up absurdities like Flat Earth^TM.
This percentage will be very tiny, but when you're dealing with a third of a billion people, even a tiny percentage ends up being something like hundreds or low thousands of people. In the year 2022, with nearly 3 decades of widespread internet use and the pervasive communication it enables, those people were bound to discover each other and reinforce their bizarre pseudoscientific beliefs.
Humans are monkeys. Monkeys aren't consistently or continuously rational. The level of and reliability of their rationality varies considerably. This cannot be changed to any significant degree.
There exists this one peculiar piece of magical thinking, of which the link is a great example. The idea that education can solve every human failing. Sometimes when people are educated, rather than making them more intelligent or more rational, you're actually only making them a more sophisticated kind of imbecile.