For Power Transformers from 132KV/220/400/765Kv the primary side vector group is designed as Y connected as in EHV system transmission is star transmission with neutral grounded.
Apart from that from Transformer manufacturer view point in Y connected system the Line oltage =1.732Phase voltage and hence there is a tremendous saving in insulation cost.
Apart from that if OLTC is provided which is generally used for Generator Transformers at 400Kv the Oltc is used in the Y connected Ckt nearest to the neutral point and hence this becomes very cheap and reliable as the volume of power handled and the voltage level is negligible.
Transformer secondary side volatges 22/15.75/13.8 etc the vector group is Delta connected.
As at this voltage the Current rating is very high and in Delta connected system the Line current=1.732Phase current and hence there is a tremendous saving in size of the conductor .
Also the Delta connected winding provides a block for 3rd Harmonic components.
This is the Practice in MRSS Main and Generator Transformers.
I work in the power sector, high voltage power stations, 110 kV-220 kV-400 kV.
1. We don't use Y/D connection for high voltage systems, we use Y/Y with grounded or isolated neutrals. The reason is that as the system topography changes in time the value for the homopolar impedance changes. This affects the ground fault current value and the overvoltage value. If the homopolar impedance is too high (that is many transformers have isolated neutrals) the ground fault current may be low, so that the breakers can handle- especially the old ones- but the overvoltage for the "healthy" phases may be too much for the level of insulation (and keep in mind that insulation is expensive fro 220 kV and 400 kV). If homopolar impedance is low than the opposite happens- high ground fault current and low overvoltage.
2. For the earthing arrangement in the power system the decisions come from the Power Management Dispatch. They have the calculations done and give orders where to ground the neutral and where to isolate it.