It's more efficient to cool and liquify air than to generate hydrogen. Store it in a container and let it expand later and you can turn a turbine. There's no issue from an environmental standpoint since you are converting air to air. You can build a cryobattery literally anywhere on earth with off the shelf components.
You're assuming that compressing and decompressing air can be done at greater efficiency. That's not that obvious, considering for example that compressing air generates heat that is always lost in the process.
