Any rocket that could deliver nuclear waste to the sun would use an awful lot of fuel, given the density of the waste, and would be a very big problem if there

Any rocket that could deliver nuclear waste to the sun would use an awful lot of fuel, given the density of the waste, and would be a very big problem if there was a failure shortly after launch. Also, anything that could deliver radioactive waste to the sun could deliver it to a major city just as easily.