[yatac42]

> but we shouldn't forget that this kind of failure can only happen starting from an ambiguous grammar specification

I don't think that's true. The following CFG is unambiguous:

  S ::= A S | A
  A ::= 'a' | 'a' 'b'

Yet if we translate this 1-to-1 to a PEG (without changing the order of the alternatives), it's not going to match any input with 'b's in it, so it doesn't match the same language.

[HelloNurse]

This grammar is difficult to adapt to ordered choice, having 4 possible variants that mostly define different languages from each other and from the "same" grammar with traditional parsing.

It's a formally very different problem from spontaneously and arbitrarily disambiguating an ambiguous grammar, but in practice it causes the same kind of suffering and it's likely to be a more common issue.