This is not a complete break. The limits of these speedups are reasonably well understood, and the literature does not indicate any mechanism that could allow further speedups for small |D|. Pairing-based cryptography relies heavily on curves where |D| is small. It is conceivable that these curves are much easier to break, but it is also conceivable that curves with large |D| are much easier to break.
there is no evidence of serious problems with either small |D| or large |D|, but the security story is more complicated for small |D|. SafeCurves therefore requires large |D|.