It'll never be safer to put that junk in a rocket. It'll never be cheaper to put that stuff in a rocket.
I was part of a group that did extensive modeling of the waste processing processes for the Hanford cleanup. One day, a coworker and I did some rough calculations based on the then-new reusable SpaceX rockets. We assumed a 50,000 lb payload, and density of concrete (assuming we'd be able to grout our waste rather than vitrify it, which is the current plan). This kept estimates unreasonably conservative.
The target: Launching our nuclear waste into the sun.
We found that with reusable rockets (5 launches per rocket) plus what we guessed to get from LEO to the sun that would be a total loss, and using an operational budget matching the current effort, we'd be rid of all the Hanford waste in under 50 years.
In that time, we'd have further developed all rocket technology, especially reusable rockets, perhaps some space elevator technology, and presumably untold numbers of additional supporting technologies.
So cheaper? Yes.
Safer? Yes, arguably. Safer in that we're done in 50 years, rather than never with the current progress. Potentially less safe in the event of a rocket exploding mid-air.