Every so often, a launch fails.
Agreed. It’s a bigger target and therefore harder to miss, there’d probably be less energy expenditure since the rocket would be drawn in by the Sun’s gravity… and hey, that thing’s gonna burn out in a few (billion) years if we don’t start refueling it!
Again, it takes more energy to send something to the Sun than to send it to Jupiter. That’s because to send something from the Earth to the Sun you’ve got to completely cancel the Earth’s orbital velocity. You can’t just point towards the Sun and drop it, because nothing in the Solar System is stationary.
A space probe launched from the Earth starts out in orbit around the Sun, in the exact same orbit as the Earth to begin with.
Anyway, the whole concept is silly. The point of sending nuclear waste off Earth would be to keep humans from ever coming into contact with it again, right? But the trouble is that rockets aren’t perfectly reliable. Far from it. So does it really seem like a good idea to stack a bunch of explosives under a load of nuclear waste? How many explosions that scatter nuclear waste over Florida can we tolerate?
If we really want to deal with nuclear waste, solidify it and bury it in a tunnel deep underground. It isn’t rocket science. Disposal of nuclear waste is a political problem, not a technological problem.