However, when interfacing to the real, non-exactly specified, incomplete information world, "good enough most of the time" is not only fine, it is all you can hope for. For example, robots that need to navigate rough terrain, or in living orgamisms at the nano-scale, or communicate in human language.
There is a huge class of things that simply cannot be addressed with the current "correct" model of computation because they are not well-specified to the lowest level in the first place.
Computers, in other words, needs to be more like brains. Yes, this does give up certain advantages, and safety guarantees. But it does not give up everything. People have trusted their life to animals and other humans, for example, for all history, even though they are far from perfectly safe and/or compliant...
(and even now, it is "fallible" humans that control the technology, so you could make a point that nothing is lost, as it was never there in the first place)