It is usual to use a 3 phase transformer that is Delta input and Star (Y) output.
If you use a Star input, you have to use a neutral connection to the star point. If not, an unbalanced load will make the star point be at some non-zero voltage and that will give too much voltage on one or two phases.
So the advantage of a Delta input is that no neutral is needed, just the three phases.
If you use a Delta output, there is no zero point to connect to earth to give a neutral, so it is impossible to run single-phase loads. Even if there are no single phase loads, the voltage to ground is not known if no point of the circuit is grounded.
Also, if the input voltages are unbalanced, it can cause circulating currents in a Delta secondary.