Why wouldn't my nuclear spaceships eject spent fuel?

In the year 2069AD, a spaceship is transporting hundreds of people in cryogenic sleep to a distant star. The spaceship engine is a nuclear fission reactor and its thruster is based on an ion drive for acceleration.

The problem is, why not dump the nuclear waste into the vast emptiness instead of threatening the crews with radiation danger? There is no legal responsibility and not even a cultural obligation to properly dispose of nuclear waste so why do people continue this perilous practice regardless of duty and border?

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Why wouldn't my nuclear spaceships eject spent fuel?

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