There's all kinds of technical reasons as well, and people love talking about space. But "five orders of magnitude in costs" seems like the conversation ends very abruptly.
So while 5 orders of magnitude makes the financial case clear, I don't have a good idea if the risks of keeping it around are potentially 6-7 orders of magnitude greater than getting rid of it.
The thing is, we transport nuclear waste over sea or air all the time, don't we? I believe the spent fuel is put into "casks" which is then loaded onto ships or jumbo jets and flown around the world.
Planes crash and ships sink, but we judge the risk (with proper pre-cautions) to be low enough when transporting radioactive waste. To me this shows that people generally accept transporting nuclear waste when the danger of catastrophe is low enough - importantly this signals that the risk only has to be low enough, it doesn't actually have to be 0.
Presumably as rocket technology advances we will eventually enter a stage similar to that in air travel, where the risk of a crash is measured in 1-per-billions rather than 1-per-hundreds or 1-per-dozens.
At that point, would we accept launching radioactive waste into space?
Also, I'll repeat that throwing away valuable nuclear material just because it's called a "waste" product is stupid. Paying a lot of money to throw it into space is even dumber.
Used nuclear fuel in those flasks are not transported trough air. Always by land or sea. On the sea they are transported in purpose-built ships.
Small amounts of highly radioactive nuclear fuel are transported trough air but they be in extremely secure type C containers that survive crash from cruising altitude. Creating similar containers that survive crash from space launch would make launching very expensive. Most of the payload would be just the container and only small amounts would be radioactive material.
It's 1000 times cheaper to recycle nuclear fuel make nuclear reactors that use nuclear waste than shoot it into space. France does it in La Hague. The rest can be buried into the ground.
Regarding price, that's quite a bit more in volume and cost than I realized. Thanks for the info!
The short answer is: Counterintuitively it would take less energy to launch a spacecraft to another star than our own sun
As for why not into the space in general:
Risk of rockets failing. Lancing probes with small nuclear batteries is controversial. Think about launching tens of tons of nuclear waste. Almost 100,000 tonnes of nuclear waste is produced per year. That's clearly too much to launch.
If we would use SpaceX Falcon Heavy to launch only the highly radioactive waste )12,000 tons per year) for $2,500 per kg. It would cost $30 billion per year and 240 Falcon Heavy launches per year. Some of them will fall down, explode etc. and that must be dealt with.
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https://www.popularmechanics.com/space/rockets/a21896/why-we...
https://www.forbes.com/sites/startswithabang/2019/09/20/this...
https://www.universetoday.com/133317/can-we-launch-nuclear-w...
https://astronomy.com/news/2016/07/heres-why-we-cant-just-ro...