I think suppressors are the victim of their own popularity, which attracted the attention of the antigunners.
The question is, why have suppressors (and SBR's) become so popular? My theory is that the gun world has become increasingly aware of the NFA, and that gradually the ownership of NFA items has come to be seen as conferring a sort of "elite" status within the gun world. Since the ownership of machine guns has largely been placed out of reach by the Hughes Amendment and the resulting price spike, people have turned to the still-affordable suppressors and SBR's. (I question their inherent value apart from bragging rights.)
This is why the antigunners are going after suppressors. (Given the right circumstances, they'll go after SBR's as well.) It's not the hardware that they hate, but the owners. Gun owners as a cultural group are the target, not so much the guns themselves.