If you are going to allow for an unbalanced steady state load (not inrush or short circuit), then it is true that you could load one wye leg to 1/3 the rating of the transformer without getting close to tripping the primary side OCPD. But that is only because that wye load would be fed equally by the two primary phases that meet at the corresponding point to the loaded wye phase wire. The energy has to come from somewhere, and that somewhere is the primary.
If you do some simple equivalent circuits, the flux in the transformer core corresponding to the single phase wye load on the secondary will be balanced by the flux from two primary windings. Because of symmetry, there should be no net current in the third primary winding.
IMHO, the possibility of unbalanced loads in general is one glaring weakness of relying on primary overcurrent protection only, but you can configure just as bad a situation with an unbalanced load on a secondary delta as on a secondary wye.
With the exception, as I said, of non-linear loads. But since the wye connection will still not have OCPD on the neutral, secondary OCPD is not guaranteed to help!