Yes, there's a 1 in 10000000 chance that 2000 years from now industrial age humans recovering from the apocalypse might dig a well in exactly that location and thousands will get sick with hundreds of deaths. You could multiply that by a hundred thousand cores and it would still be negligible compared to the hundreds of millions likely to die due to climate change in the next century
But what about if we had a Reactor Dump storing 100's of these reactors, and then something happened to that dump, either it was hit by a meter or it was intentionally attacked in some way. Could that result in an apocalyptical type event?
It would basically be a few Chernobyls in the worst case (a 1 in 1000 year asteroid impact winning the 1 in 100 million lottery and hitting the dump) and that mostly means extra birth defects and cancer (you wouldn't want to live somewhere that gave you a 10% chance if dying due to cancer age 40, but you could still have a civilization in such a location). It doesn't end life in the impacted area.
For intentional attacks there are much much easier ways of killing a lot of people.
You cannot do that. There is no place on Earth that we can be sure is geologically stable over that time period.
What a selfish thing to do: Make future generations pay for our current consumption for millennia.
Makes no sense to me, but my physics education was decades ago
The half life of most of the waste product from a gen-3 uranium reactor is measured in millions of years (235U's half life is ~700 million years, for example).
In some gen-4 molten salt reactor designs, most of the waste product would have a half life measured in hours, so they wouldn't need to be put into long-term containment at all. And the rest of the waste products would only require a few hundred years before they are emitting only background level radiation.
Hopefully someone with actual education on this can give a more complete answer, but that's my Reader's Digest understanding.
The metal containing the molten salts might become somewhat radioactive too.
All in all, this is still comparable in amount of waste to water cooled reactors.