The reason I picked Black is because of his unusual but distinctive singing voice. The music of Hedwig is rooted mostly in metal and grunge, but JCM had an indie voice like Lou Reed, and the actors who followed him had a more theatrical sound. Stephen Trask, on his tracks in the soundtrack, could be a Ben Folds wannabe.
With Black's ties to metal and grunge performance, he could bring a strong new vocal sound, potentially more authentic than some of the non-Mitchell, non-Trask performers. What he lacks, however, is a strong tie (either membership or affiliation) to the queer community, which seems to be something of a prerequisite for the role.