I keep asking this question:
"Hot" nuclear waste means theres still a lot of energy left to capture. Why are we disposing of materials that still have a lot of energy to capture? Seems like the closer we get to lead, in terms of capture, the better.
It would be like taking my half-full of gas car to the pump, dumping the existing gas, and getting fresh. Its a waste of energy, waste of resources, and generates worse nuclear waste.
There’s a lot of nuance to the answer and I’m not a nuclear engineer, just an EE and occasional nuclear enthusiast. The biggest issue is the cost-effectiveness of reprocessing the “waste”, which you are completely correct about still having a ton of residual energy available, back into a useable fuel for a sustained nuclear chain reaction.
Some of the fission products that are produced in reactors are actively harmful for sustaining a chain reaction (neutron poisons), Xenon-135 being a prime example. Xenon-135 only has a half-life of about 9 hours (which means it’s pretty spicy) but it also has a massive neutron capture cross-section. If it doesn’t capture a neutron, it emits a beta particle (electron/positron), which doesn’t contribute to sustaining the reaction; if it does capture a neutron it becomes Xenon-136 which is pretty stable. In both cases, it’s sitting in the fuel but either useless (yay) or actively hurting the neutron economy (boo).
At some point in the future it might be economically advantageous to reprocess “used once” nuclear waste and use it in a second cycle but for now it’s way cheaper to get more fresh uranium and process that into fuel instead.
That's not what "hot" means in this context. "Hot" means "highly radioactive", i.e. high number of decay events per second, high concentration of short half-life isotopes, high power/volume resulting from radioactive decay.
Nuclear reactors do not work off radioactive decay. U-235, for example has a half life of 704 million years. Radioisotope thermal electric generators [0] by contrast do run off radioactive decay, an isotopes used for that application have short half-lives, such as Pu-238 with 87.7 years.
Commercial nuclear reactors use unenriched or minimally enriched fuel. This means that, within a fairly short period of time, the percentage of fissile material in the fuel drops to the point where continuing to use it is no longer economical. At that point the fuel is a mixture of extremely hot fission products, transuranics, unreacted fuel, and non-fissile (but fertile) isotopes such as U-238.
It's not practical to use the decay energy from the fission products for power. What would make much more sense would be to remove the fission products and recycle the fuel that remains into new fuel (for a reactor that's designed to use it). This would be a much more efficient use of mined nuclear fuel (allowing nuclear power to be used for thousands of years), it would vastly reduce the volume of nuclear waste, and it would mean nuclear waste would only be hazardous for decades to centuries.
The US was on the path to this with the Integral Fast Reactor and Pyroprocessing [1] developed by the Argonne National Laboratory. This was killed [2] in 1994 by the Clinton administration. Not for any technical reason, but because it was a "threat to nuclear non-proliferation". How that makes sense when, to the best of my knowledge the process developed by Argonne couldn't be used to produce weapons-grade material, and even if it could the US already had nuclear weapons so it wouldn't be proliferating it to a non-nuclear country, I don't know. But, apparently, since some other forms of nuclear waste reprocessing can be used to generate weapons-grade material (by extracting Pu-239), it was a bad symbol so it had to go.
[0]: https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_ge...
[1]: https://en.wikipedia.org/w/index.php?title=Integral_fast_rea...
[2]: https://en.wikipedia.org/w/index.php?title=Integral_fast_rea...
They just don't produce that much power. We're talking about hundreds of watts per barrel. You can get more energy by putting a water barrel on your roof.
And in this case, the reaction had nothing to do with nuclear energy. It was a regular chemical reaction, that got into thermal runaway.
The materials are still full of potential energy, but it's much more expensive to reprocess them than to mine fresh uranium. It's even more expensive to reprocess them without incidentally releasing more radioactive contamination into the environment. (Several countries reprocess nuclear fuel now or did so in the past, but the facilities have always released more radioactive material into the environment than simple storage.)
It's kind of like why old and broken polyvinyl chloride pipes go to landfills instead of being burned as fuel in power plants. Even though PVC is flammable, the cost of burning PVC and capturing its carcinogenic combustion byproducts is a lot greater than burying waste PVC and burning fossil hydrocarbons.
In the far future, uranium mining costs might rise enough that it makes economic sense to reprocess old spent nuclear fuel. In the early days of the atomic age people thought that reprocessing and breeder reactors would be necessary because uranium was believed to be very rare on Earth. Vigorous exploration programs and new mining techniques proved this belief to be false by the end of the 1960s, and the situation hasn't changed since then. It's safer and cheaper to mine fresh fuel and just store the old fuel without any sort of reprocessing.
See e.g.
Bunn, Matthew G., Steve Fetter, John P. Holdren, and Bob van der Zwaan. 2003. The Economics of Reprocessing vs. Direct Disposal of Spent Nuclear Fuel (PDF):
https://dash.harvard.edu/server/api/core/bitstreams/7312037d...