In fact, Von Neumann proved mathematically that it's possible to build a reliable system out of unreliable components. But, modern digital logic uses a simpler

In fact, Von Neumann proved mathematically that it's possible to build a reliable system out of unreliable components. But, modern digital logic uses a simpler mechanism: the thing you are missing is that noise does not propagate or accumulate in discretize (digital) systems, as long as it remains below a threshold, and circuits are designed so that it is far below the threshold.