Whereas, with a quantified probability of traitors (e.g. hardware MTBF), the risk of Byzantine fault is computed. Which was the intent of Lamport et al's paper.
That's not really the case. Read the paper more carefully. Simple probabilistic hardware failure is easy to cope with using redundancy and majority voting. The hard problem is failures that are more subtle and complex, which can mimic deception and collusion.
The algorithm becomes a tool in a toolbox which is used to improve robustness against certain types of failures, but the robustness is still never absolute, and in real systems the actual probability of failure is still not known.
I suggest you also read the paper more carefully. Specifically Section
"6. Reliable Systems" which we are referring to.
What it says is that as the hardware fails the outputs can become like traitor inputs to other hardware components causing the cascade to lie, which is precisely the BGP problem and what the solution is modeling by a count of traitors (
passing along a traitor's lie doesn't create a new traitor). Even in the case where the derivative computation is corrupted due to the corrupted input, this is still a quantified probability of cascade of traitors obtainable from engineering and math/models applied from hardware MTBF rates. It is more exact science or estimation than not knowing. There is no decentralization, Sybil attacked introduced which otherwise makes the estimation highly unknowable and unmeasurable (science requires measurement to validate that models are predictive).