Interestingly, the same effect shows up in communications systems. The more efficient an error correction code (ie. the closer it approaches the Shannon Bound), the more catastrophically it fails when the channel capacity is reached. The "perfect" code delivers no errors up until the Shannon bound then meaningless garble (50% error rate) beyond the Shannon Bound.

My point is that error correction codes have a precise mathematical definition and have been deeply studied. Maybe there is a general principle at work in the wider world, and it is amenable to a precise proof and analysis? (My guess is that mileage may be made by applying Information Theory, as used to analyse error correcting codes.)