I think one key aspect is that they are less susceptible / immune to loss of coolant incidents. In a PWR if there is a loss of pressure, or coolant in any other way, and emergency cooling doesn't work, the core overheats and might melt down.

An uncooled pool of molten salt will keep on generating heat even after the reaction is stopped, so will continue heating up, but it is possible to design the reactor so that the whole thing remains stable. Since the pressure is low, there is no risk of explosion, or release of the radioactive materials.

So the energy density is i think a secondary benefit, if at all.