What are the Pros/Cons on the 30 Degree voltage phase shift between the primary and secondary of a Delta-Wye Transformer

I have searched this wonderfully informative website and learned much about Delta-Wye connections and why a phase shift in voltage would exist between the two. I am also aware that both Delta-Delta and Wye-Wye connections do not have this phase shift. My questions is: What is so important about this phase shift? Are there Pros/Cons?