Is the prohibition on new clothes during the year of mourning for a parent arise because you are not supposed ton say a shehecheyanu or is there another reason?
A mourner is allowed to say the bracha of shehecheyanu.
The prohibition of new clothes for 30 days, and the custom of refraining for the entire 12 months is part of the general laws of aveilus which minimize the simcha of the avel during this time.
The custom is to be lenient to allow others to wear the new clothing first, and thus permit it for the mourner.
Magen AVraham 551:42, Mishna Brura ibid. s”k 98.
Ramam Y:D 389:3.