Green energy is sustainable energy. The use of chemical batteries for energy storage is neither green nor sustainable.
Chemical batteries are made of dangerous rare-earth and caustic materials that are mined and extracted from unstable regions of the world where people are worked to excess for very minimal pay, and often without basic health and safety protections.
The life cycle of chemical batteries from rare-earth extraction, to manufacturing, to use, to end of life recycling or disposal, is costly and carries significant dangers. If you build a product with dangerous materials you have to dispose of a product with dangerous materials.
Chemical batteries have a long tail of issues – lead-acid batteries outgas sulfuric gas and have lead plates, and require perpetual nanny maintenance to keep them operating effectively. Lithium-based batteries are so chemically reactive they pose fire and explosion risks. Other than very small personal computing devices, lithium-based batteries cannot be transported by air. Even road transit requires special handling certifications and training to move them. Both battery systems require extensive mitigations for safe handling and fire suppression.
Supercaps are manufactured with readily available graphite products that represent little environmental impact. Because their useful lifespan is many times longer than chemical batteries they do not to be replaced as often, and when it is time to dispose of them they are readily recyclable.
When Supercaps are partnered with sustainable energy sources like solar, wind, and hydro, the system is incredibly green, long-lived, and recyclable.