Extremely. For instance, in Washington state, the BPA just had a 10-day wind lull. The 4 GWe of capacity was at a standstill. It would have taken batteries covering an American football field (with end-zones) 100 stories tall and costing $90B to fill that gap [1]. The mining and carbon footprint of that energy storage system would be very non-trivial. Pumped hydro storage is no good either due to biogenic methane in the reservoir.
[1] https://partofthething.com/thoughts/a-medium-length-primer-o...