The resulting picture for

The S-wave decay amplitude primarily arises from a ss contribution.
For the D+ the ss contribution competes with a dd contribution.
Rather than coupling to an S-wave dipion, the dd piece prefers to couple to a vector state like (770), that alone accounts for about 30 % of the D+ decay.
This interpretation also bears on the role of the annihilation diagram in the Ds+   decay
the S-wave annihilation contribution is negligible over much of the dipion mass spectrum. It might be interesting to search for annihilation contributions in higher spin channels, such as 0(1450) and f2(1270)

The S-wave decay amplitude primarily arises from a ss contribution.