Storage (especially at the current rate of growth) is nowhere close to meeting our capacity needs for a 100% renewable grid. We can't store enough energy for a single day of consumption. Keep in mind we would need to store enough energy to handle long periods of low production. We're an order of magnitude away from that. On top of that, the vast majority of global energy storage is not actually provided by batteries, but by pumped-storage hydro (expanding this capacity would run into environmental issues and physical limitations; we don't have enough water in convenient locations).
Battery tech seems way off from providing us the needed capacity. Even Tesla is bottlenecked by battery production. We'd need to see Moore's Law level growth to have enough storage capacity to mitigate climate change, but we're only seeing 30% to 40% growth, which is just not enough given that it's currently less than a fraction of a percent of our total energy storage needs for 100% renewable power.
People are also seriously overestimating the time table needed to build a nuclear power plant. India, China, and Russia have been able to build plants in a few years vs 10 years in the West. If we're not pushing nuclear now, we'll be burning coal and natural gas for the next century.