The stuff that is heavier than water ends up in the river delta, everything else dilutes into the ocean. Once it’s in the ocean, there’s not much humans can do about it. Promoting populations of sea grass and filter feeders like mussels can at least capture pollution in a form that settles to the seabed and improves water quality.
There will be pockets of pollution that persist for a long time, and floodwaters could stir some of that back up, but the above poster is correct. Cleaning up a river can be as simple as stopping the sources of the pollution. A dirty river is dirty because stuff keeps getting added to it. Of course stopping sources of pollution is way easier said than done.
The other benefit I can think of is keeping the fissile materials always sub critical. You don’t have to worry about a meltdown if the reaction is not self-sustaining. It’s an odd marrying of technologies, but I think people are being too dismissive.
Although, I wonder if the true purpose of such a device would be high output breeding of fuel for weapons use.