What could possibly go wrong.

>"This is the right solution"

...may not be the correct decision.

Sending it into the sun could be a solution for a lot of our waste. But I wonder if the energy we need to produce/spend to first launch all of it into our orbit won't create more problems than what we're trying to get rid of.

You want to put a large amount of highly radioactive waste on top of a couple of tons of highly explosive rocket fuel? What could possibly go wrong?

Putting it deep underground is the safer option.

Not a couple of tons, thousands and thousands of tons. A rocket to move any significant mass of waste to the sun (far more delta-v than getting to the moon, or escaping the solar system), without decades-long journeys [1] would make Saturn V and Starship look like toys, or if would be a very complex asssemble-in-orbit deal.

[1] you can use gravity assists like the Parker Solar Probe, or go very, very far out, make a small adjustment and then fall back in for about 1/3 the total delta-v.

Don't worry, Sun will consume these rods at right time in the future, with rest of our plant. We don't need to store this waste indefinitely. We need to keep it safe just for few billions years.

Even if you wanted to put a bunch of very radioactive waste on a rocket which might not necessarily make it away from Earth, it'd be very wasteful of fuel to shoot it into the sun compared to shooting it out of the solar system.

To get something to fall into the sun rather than just carry on orbiting it you need it to lose the velocity it has by virtue of being launched from Earth, if you just punt it into interstellar space on the other hand you need a lot less fuel and you can get a boost from the planets if you line it up right.

Launch Nucler Waste on top of Rockets? What could go wrong?

"Space Launch Vehicle Reliability" - https://www.tech-insider.org/related/research/2001/0301.html

"Of the 4378 space launches conducted worldwide between 1957 and 1999, 390 launches failed (the success rate was 91.1 percent)"

kurzgesagt has a video on this: https://www.youtube.com/watch?v=Us2Z-WC9rao