The capital cost estimates for solar and wind almost always conveniently ignore that simple fact.
It's not well known that coal fired power plants must have energy storage, too. But they store the raw fuel (coal) on the ground BEFORE it is converted to electricity. This is so the plant can get through freezes in winter, winter transportation disruptions, and labor disputes. Coal piles can typically feed a power plant for 90 days. The biggest battery storage systems today (all demonstration projects) can store the output of a large power plant for a few minutes at most.
Yes, that is why goal and gas need to be continuously run, even if at modest levels assuming solar can be made somewhat successful. You can’t just switch them off and on whenever you need them. They need to keep running much like oil rigs in Siberia. They can’t stop them in winter regardless of the price of oil because they will just freeze up. They have to pump all winter or risk being frozen up or damaged.