A good question.
With a balanced delta load there will be no current in the wye point. And with an unbalanced line to line load the load current will be supplied in parallel by the obvious winding and the series combination of the other two windings. The sum of those two primary winding currents will balance the current at the wye point to zero.
Now look only at the unloaded transformer. If the voltages on the wye side are not perfectly balanced you will get a circulating current in the closed delta side sufficient to bring the system into balance. This will result in a very high neutral current in the wye side, possibly greater than the transformer capacity would suggest at full load.
If the wye point is left unconnected the applied primary voltages will simply be brought into balance as the wye point floats relative to ground.
With a wye wye transformer there is no balance condition imposed on the output and the vector triangle on the output will automatically be closed, even if unbalanced.
You can see this more easily if you look at what happens with unloaded wye delta and unloaded wye wye when the applied voltages on the primary are 120, 120, and 0. (Line to neutral)