I enjoyed this in the reddit post as well|
Your friend who said the reason was purely financial is right … but may have failed to make the point strongly enough.
The Earth is in orbit around the sun. That means the Earth, and everything on it, is moving through space at about seventy thousand miles an hour. In order to drop something into the sun, you'd have to bring it to what is effectively a dead stop in space, which means accelerating it from rest to seventy thousand miles an hour going in the direction opposite the Earth's orbital motion.
That's twice the velocity necessary to fling something out of the solar system entirely. Now, we have launched a rocket to solar escape velocity before, about 35,000 miles an hour … but only once in all of human history, and doing so required a custom-assembled rocket and more than two hundred million US dollars, and the total payload was still only about a thousand pounds. And that's half of what we'd have to do, in terms of total velocity, to fire a payload of the same size into the sun … and rockets don't scale linearly with final velocity but rather exponentially, meaning the cost of putting a thousand-pound payload into the sun would probably be on the order of a billion US dollars, not counting the up-front R&D costs.
And did I mention that spent nuclear fuel is among the densest stuff on our planet? A cubic foot of the stuff weights more than a thousand pounds — 1,189 pounds, to be precise.
"Purely financial" doesn't even begin to cover it. To put any useful amount of the stuff into the sun would literally cost more than the total amount of money in the whole world.