>hydrogen's big advantage -- the low cost of storing it
Hydrogen by its very nature, due to it being the smallest atom, embeds itself into the walls of its container. It will rot the metal walls you use to hold it long term.
It's stored underground in caverns, not in metal pressure vessels. This is a demonstrated technology. It's also the same way natural gas is stored. The cheapest option is solution mined cavities in salt formations. Europe (for example) has enough salt formations to store many petawatt hours of hydrogen.