Alternatively: the spike in demand will result in a similar spike in production capacity, leading to overall lower prices due to better economies of scale.

Battery costs have declined by 99% in three decades. Solar isn't much different. Demand for both have exploded during that time period.

Besides, the current battery storage tech is just a side-product of the EV revolution. If grid battery storage becomes the main solution we'll undoubtedly see cheaper and easier-to-scale alternative tech like iron redox flow batteries be adopted. Bulky, lossy, impossible to transport? Don't care - it's cheap!