There are a few reasons why this is a bad idea:

1) Launch failure could scatter nuclear waste over a large area

2) It takes a LOT of delta-V to fire something into the sun. It took the world's most powerful rocket to put the Parker Solar Probe even close to the sun and that was only 700kg.

3) If it doesn't get to the sun it could easily return to Earth accidentally.

For anyone curious in gaining a more intuitive understanding of this good answer, I highly recommend playing a few hours of Kerbal Space Program. Hitting the sun is both hard and expensive: things in orbit want to stay in orbit, so it takes a lot of energy to change orbits. (And you're likely to have a few rockets explode within the atmosphere as you attempt)

The smartphone game Osmos really brings orbital mechanics into hand, in a fun/mindless way.

2) It's actually a lot easier to speed something up enough to eject it from the solar system than it is to slow it down enough to let it fall into the Sun. the first is only 18 km/s but the later is 30 and with the tyranny of the rocket equation every bit of delta-v is harder than the last.

Orbits are very non-intuitive until you've had a chance to play around with them, KSP did wonders for my understanding of orbits. Lots of people make the mistake that once you're in orbit you can just freely move in 3D to wherever you want a perception not helped by the number of times movies show it working that way.

1. There’s extra danger every time nuclear material is launched on a satellite, be it for a thermal generator like on the Curiosity rover, or some failed tests the USA did on Pacific islands in the 60s as part of Operation Fishbowl that resulted in a large amount of waste spread downwind. 2. No satellites can actually reach the sun - to do so, anything launched from Eart would need to cancel the forward velocity to force its orbit to “fall” into the Sun. This is such a high number that it’d be cost prohibitive for the amount of fuel and size of launch vehicle required.

Ever heard of a gravitational slingshot?

We aren't exploding the nuclear waste in the form of a bomb when we launch it via satellite. It could also just fall into the ocean in case of a failed launch, where it probably won't be a problem.

A gravitational slingshot short of Jupiter would not suffice, and maybe not then.

I'm not experienced in this but if there was a launch failure isn't that basically a dirty bomb?

That's the issue exactly. Many things can go wrong if you place a lot of radioactive material on top of liquid hydrogen and liquid oxygen tanks.

Not if it's built correctly. The problem is that would be weight-prohibitive (vs. putting a small nuclear thermoelectric generator into a very tough housing, which has been done for years).

yes, I can take that as an answer:)

Because it's a lot cheaper to bury it in bedrock, and it's just as safe. The scenarios in which underground storage lead to contamination are borderline hyperbolic: some sort of collapse leads society to lose all records of waste storage locations, some future society miraculously decide to dig right where the waste was buries, and lastly said future society is too dumb to realize the waste is poisonous (yet advanced enough to dig through a kilometer of bedrock).

I think the assumption is that after 10000+ years society, government, and historical records available are complete unknowns.

And the point remains, what is the likelihood that some future civilization is going to happen to dig in the _exact_ spot where the waste was buried? And, if they're capable of tunneling through a mile of bedrock, wouldn't they have the smarts to notice that the stuff in those casks was poisonous?

Everything on Earth is currently moving at about 30km per second (over 100,000 km/h). So first you need to boost it out of the Earth's gravity well, then you need to decelerate it to near zero from 30km/s. It's easier to send things to other planets than to the sun.

The first thing that comes to mind is the risk of wide-area contamination if a rocket explodes.

Because rocket launches are politically problematic as is.

That’s why the US launches from Cape Canaveral (avoids all land), and Russia launches from Baikonur in Kazakhstan (avoids Chinese airspace).

Now imagine not only launching rockets, but nuclear rockets. ”Hello Mr Putin, yeah the rocket we’ve launched, it only contains nuclear waste, not nuclear weapons, we promise!”