If rockets are reliable, can we throw our nuclear wastes towards the sun? The sun's gravity and it's internal energy will do the rest.
Could we? Yes. Should we? Absolutely not! Why?
- The energy required to send something to the Sun is REALLY high. Like, we can't even really send any payload there at all. Before doing that, crashing it in to the Moon would be just as good and keep it secure. Or Venus, if we wanted to send it to somewhere we probably won't ever get to.
- Rocket launches don't have a 100% success rate. If the rocket exploded, well, there's a radioactive wasteland, which is WAY worse than the problem that we have now.
- Radioactive material might some day be useful on Earth. Most of the problems with disposing of it are assuming that we might want to get access to it sometime in the next few hundred years, but not after.
Really there is actual useful energy left in nuclear waste, but launching in in to space is WAY too risky.