Batteries are big, expensive, and inefficient. Then, when they're worn out, you have a toxic mess to recycle and a lot of chemicals to dispose of. Bad.
Lithium isn't big, I can buy it now for about $150/kWh, large scale buyers are down to about $100/kWh, they are not a "toxic mess" to recycle or otherwise and the are not bad. They also demonstrate extremely high levels of round trip efficiency - especially in comparison to photosynthesis.
Storage and transport of H2 is Extremely difficult.
Over production for storage is a given, but the technologies that are out there are pulling us away from hydrogen.