Light water reactors were "fail safe by design" when they were introduced in the 1950s and 1960s. And actually their safety record is far better than that of any other industry.
But that ain't good enough when the results of those rare failures are so devastating.
So basically "fail safe by design" is not anywhere good enough when it comes to nuclear power facilities. The damn things need to be fail safe in practice-- and not only do we not know how to do that, nobody knows how to learn how to do that. For one thing, humans are a critical part of the operation of any of these things, and we do not have a clue about how to design a reliable human being, let alone how to construct one.
Case in point: pebble bed reactors look good on paper, but rubbing those balls against each other is going to create dust, and no one knows how that dust is going to behave during long term exposure to 1500 degree temperatures. Our materials science doesn't cover that. Nor can it, not with any kind of reliability. At a guess, if any of that dust came in contact with air before it cooled to less than ten times ambient temperature, it would explode like gun powder. And that's just the safety cladding. Underneath that candy coated shell is a pyrolitic material whose behavior in moist air is quite similar to anti-tank and bunker-busting ordinance.
So how can anyone develop a safe design when it involves an environment so alien that we cannot reproduce it? Or even develop sensors that could say what it is doing if we could somehow mimic it? Talk about black boxes. "Fail safe by design" has no meaning in these conditions.