Good discussion going on here, I like it when these kinds of questions are raised as it makes you reassess your thoughts which is always a useful exercise.
I did some more digging.
From the Spanish tower Data the towers can operate 24/7 with seasonal output variations. There is day vs night difference. Peak power in summer months and lowest output in winter months, no surprise there. The day vs night output varies from very little in summer to about 30-40% (my own suspect back of envelope calculation) drop at night in Spring and Winter. Adding power storage would no doubt iron out the day vs night output when needed in the less sunny months.
However If built somewhere that has 365 days of good sunlight that can emulate or exceed the Spanish summer then I don't think storage would be a given as there is little difference between day and night power generation. There are plenty of deserts around the world that would fit that profile. See Summer graph from the Spanish project.
If storage was still deemed necessary regardless as suggested, then considering the 24/7 operations and minimal loss at night , storage may only have to be a fraction of that required by other renewables that have to cover 100% loss at night or during no or low wind/wave conditions. This would be a considerable upfront and ongoing cost saving over other renewables over the life of the plant.
A little cut and paste from the Spain project, bold is them not me.
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Detailed investigations, supported by extensive wind tunnel experiments, show that
thermodynamic calculations for collector, tower and turbine are very reliable for large plants as well.
Measurements taken from the experimental plant in Manzanares
and solar updraft tower thermodynamic behavior simulation codes are used to design large plants with an output of up to 200 MW.
This plant without additional storage operates 24h per day, but at significantly reduced output during the night, especially in winter.