Energy density is more a problem of materials. If you start talking GW hours it’s ~1GW from a ~38 ft tall and 48 meter diameter tank, even at $1,000 per ton it adds up. On top of that you need steam turbines etc.
Think of it like a scaled up, reversible refrigerator.
I'd like to know if they also have a 'medium temp' tank, since if they do, they can keep the temperatures of the hot and cold tanks constant, and just change the amount of molten salt in them. That in turn means the compressors can be fixed compression ratios, which will dramatically increase efficiency.
The paper suggests changing the pressure of the working fluid to adjust load, but I suspect it is hard to design a turbine to be efficient at a wide range of working pressures, so instead they'll end up with many parallel turbines, and just switch some off to get less energy produced.
You produce energy at an amortized cost of $X /MW. You store energy efficiently (lithium batteries) at an amortized cost of $Y /MW back into the grid. You store energy inefficiently (Malta?) at an amortized cost of $Z /MW back into the grid.
If Z<< Y, then simply ramp up your input production and you are likely in the money. Also, I'm not sure what you mean by "Worse heat has fairly low energy density and cools over time"... energy density is not relevant at all when you have practically unlimited space to store power (GIANT) fields next to your solar/wind farms.