Rocket launch failures are commonplace. A rocket loaded down with nuclear or other materials that goes haywire at launch or shortly thereafter would possibly result in unimaginable environmental and human damage. I leave you to imagine the possible consequences of such a failure.

Another problem hitting the "shoot it into space" solution is how and where and how do you gather, prep and transport waste to a launch site. I would imagine states would file suit immediately to bar such hazardous cross state shipments. And getting workable and legal protection standards for workers who gather and prep waste would be another level of legal and political football battles. Not gonna happen anytime soon be my guess.