What benefit do you see in comparison for design?
I don’t think comparison is the issue. Rather it is finding the commonalities of thinking across disciplines and differentiating the situations in which the commonalities are applied.
 
Is PHD design study accepted and validated, or is it an ongoing struggle to justify the academic side of design?
PhD design study should be accepted and validated on the basis of what it can contribute to an understanding of design thought and practice, not on whether it justifies the academic side of design (which has its own struggle to contribute to the education of us all.) Any study is justified (or not) by what it can contribute to the underrstanding of the concerns it is focussed on.
 
What risk is there in comparing design studies to something as applied as investigation (criminal or otherwise - accident investigation is similarly teleological and generates new areas of knowledge simultaneously.)?

I can see no risk except that of failing to see how the information being considered informs (helps to resolve) the situation of concern.