Maybe it would need more energy for cooling than what it generates? So it would have to be scaled up to a size where the surface-to-content ratio becomes favourable. There might not be enough salt for that :-)
If I recall the video correctly, solid metal oxide fuel produces offgas at a 50:1 ratio, while being insanely dense. This produces pretty insane internal pressures if the goal of the fuel design is to keep everything contained. Like strong enough to eventually cause mechanical failure of the fuel.
I think there's a lot of really difficult constraints intersecting in these fuel assembly designs, and something that seems obviously simple probably isn't.
Ideally you wouldn't need to expend energy to keep the coolant cold enough; rather, you'd use the coolant to boil water to run your steam generator.
I'm sure there's all sorts of practical reasons why that wouldn't work, but it's an interesting thing to think about.