I imagine that someone will discover a better way to dispose or "recycle" nuclear material before that.
Another issue is the reliability of your launch vehicle. Sometimes these things blow up on launch, which you really don't want happening when it's loaded with radioactive waste. Developments made by SpaceX might contribute positively to both of these, by lowering the cost and increasing the reliability.
A third issue is that this stuff might turn out to be valuable after all. Hopefully not for making bombs, but future technology might come up with socially positive uses for material that's currently considered dangerous waste.
Sure. Lots of people can imagine all kinds of things. It's all wishful thinking though, where they're hoping someone else will solve the problem for them.
We need actual solutions in order for it to be feasible, not wishful thinking.
There is a context on this [1].
[1] https://en.wikipedia.org/wiki/Advanced_reprocessing_of_spent...
[2] https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=repr...
It's good that science is developing potential solutions to the problem. When (and if) they do come up with a good solution, then it will be the right time to consider the pro-nuclear approach.