(My Follow Up Post:) - SpaceX wouldn't have to eliminate annual world-wide radioactive waste all at once per year, the process can and would have to start out small and local-scale. On google search I got "2000 tons of radioactive waste produced" in the U.S. alone. I think starting with a fraction of that number would be good to start with. Instead of the unfathomable-herculean-insurmountable-impossible 1000 extra F9 ASDS launches per year for $50 Billion, it could start at an extra 5 F9 ASDS flights per year to start off - marking that price down to around $250 million per year for the elimination of at most 60 tons anually to LEO. If you brought that to HEO, by the subreddit moderator's estimation, that would be $2.5 Billion per year instead (which could be split paid between SpaceX, NASA/Government funding, and Elon Musk himself). With Starship, you could bring that flight number down to maybe 2-3 extra launches per year and On such a small scale it might even be possible to go even beyond HEO. Keep in mind the numbers (launches and cost) are not static, they can be adjusted to whatever is most affordable (e.g. whatever optimal amount SpaceX could reasonable get beyond HEO). The important thing at first is that it gets done and SpaceX shows the world it's possible.
As for your concern about the "Not In My Backyard" argument in regards to launches failing and crashing with radioactive debris falling, the answer is quite simple: "Nuclear Waste Transport Dry Casks". Those things are as close to indestructible as any container that humanity has ever built. In test simulations they've been repeatedly run over by fully loaded cargo trains weighing more than 18,000 tons at top speed of 50-60mph and the casks came out hardly scratched. (I'll link below)
As of 2018 it will collectively cost tax payers $493.96 billion dollars over the next 50 years to clean up America's total nuclear waste. This Price is increasing dramatically over time and the amount of radioactive waste on hand at any time fluctuates relative to the amount produced by nuclear power plants per year (I'll link NBCNews article below). YES - In terms of price using rockets to dispose of nuclear radioactive waste compared to drilling holes would be inefficient at first, but there are two significant advantages SpaceX would have in this situation -
1.) Time. The vast majority of nuclear waste created per year is not burried, it is simply contained and kept on-site in afore mentioned Dry Casks since there is nowhere to put it most of the time since drilling costs money and time and is difficult. Because of this, it doesn't need to be taken all at once but rather in a gradual more affordable process. While it MAY cost more right now to get rid of the waste via F9/Starship launches it would still be a better far more permanent way of getting rid of any radioactive materials. On top of all of that, the steadily decreasing price of space travel/tons-to-orbit over time would also be on our side and make it more affordable to carry more massive and/or more frequent payloads in the coming decades and making it a preferable alternative. In contrast while the price of digging deep holes underground is cheaper and probably isn't going to change all that much going into the future it still takes a lot more time and is much more difficult to accomplish than a rocket launch. To top it all off the more we use Nuclear Power the more radioactive waste will accumulate faster than we can bury it and the downside is that the material would still be on Earth. No matter how well contained in Dry Casks, people won't like that and it will work against the good image of nuclear fission power.
2.) A better public perception of eliminating nuclear waste permanently and therefore incentivized use of Nuclear Power. This is the primary short term goal. The process of actually pulling it off would show the world (and more importantly the government) at the very least that it's a possibility of disposal and make nuclear fission power perceptually more appealing and, given enough time with enough rockets, we could eventually get rid of all of it if need be. This in turn would cause investments in building more rockets to further accumulate, more widespread utilitarian demand for the creation of more rockets, and specific infrastructure of disposal transport to grow. New rockets built could obviously be used for more than just disposal - (e.g. sattelites, astronauts, scientific equipment, oxygen, etc...). By extention this would expedite lowering the costs of space travel even more and increase demand for more rocket engineers/technicians/experts making such careers generally more appealing for STEM focused undergraduates to major in. The system would essentially feed itself by having a positive trend of growth for the industry as a whole.
Remember: The ultimate goal is not specifically to eliminate nuclear waste, as I said previously, we can do that fairly efficiently. This is a matter of Public Perception. The ultimate long term goals for the the entire undertaking would be to expand the Nuclear Power Industry by means of public perception shift to combat Global Warming and provide clean energy, expand the demand of Tesla/Electric vehicles due to increased Nuclear Power Usage, and to exponentially expand the Rocket Building Industry in manufacturing scale and quantity produced with higher government funding while simultaneously helping to decrease the price of space travel. Moving larger payloads of radioactive waste over time would just be the catalyst of it all while the actual disposal of said waste would be a side perk.
I would like to say that while I am not personally a technical expert nor do I have the specific numbers of all costs that would be involved, I think that under the right direction and management with the the right skills and information this idea might have significant synergetic potential between SpaceX & Tesla to do a lot of good for both companies, their industries, and the world. If I end up being wrong then I welcome the learning experience and will find a different direction to go. If I'm right I can only hope this idea can get into the hands of the right people.
Links:
https://www.nbcnews.com/news/all/cost-taxpayers-clean-nuclear-waste-jumps-100-billion-year-n963586