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.
The issue is that it's a waste of resources. A dam is harnessing energy from the rainfall over hundreds to thousands of square miles of land area. So the resources required to build it, even though large, are very efficiently used over decades of use.
A tiny system uses orders of magnitude less materials but harvests many orders of magnitude less power. A tiny system probably isn't going to ever generate more energy than it took to manufacture.
Systems like this are at best a novelty. We need to all be wary of greenwashed scams, and this is one of them.