An explanation of the OZI rule can be seen from the decrease of the coupling constant in QCD with increasing energy (or momentum transfer).
Another explanation of the OZI rule comes from the large-Nc limit, in which the number of colors Nc is assumed to be infinite.
For states lighter than the charged D mesons, the decay must proceed just like the above example into three pions, with three virtual gluons mediating the interaction, each of which must have enough energy to produce a quark-antiquark pair.
In this case, only two gluons are required, which share the energy of the light quark-antiquark pair that is spontaneously nucleated.
The suppression arises from both the smaller values of the QCD coupling constant at high energies, as well as the greater number of interaction vertices.