It takes a lot of delta-v to slow something enough for it to drop into the Sun. Big delta-v means lots of energy means lots of money. It'd be much more efficient to launch something out beyond or inside of the Earth's orbit around the Sun.

Of course, the idea is asinine because of the risk of launch failure. It's one thing to launch a small radio isotope thermal generator that has been harded and tested to withstand any possible launch accident. It's another thing to try it with bulk waste. If you built the bulk waste container as strong as those generators, then the amount of radioactive material you could launch would be small.