Storing it in the desert (or on site) is many orders of magnitude safer than shooting it into space. Not to mention the massive energy requirements for launching items into the sun. In fact it takes far more energy to reach the sun than it takes to escape the solar system entirely.

The simple fact here is that storage of nuclear waste is not a practical or safety issue at all, it's a political issue. If we can shut down the NIMBYS and irrational anti-nuclear activists this issue will be solved forever.

We don't need innovative solutions on handling the waste (that's already a solved issue), we need innovate solutions on getting political support for it.