BTW, hydrogen-air battery = hydrogen fuel cell, if you didn't realize that.
Basically, if you're cycling regularly (e.g. smoothing solar and wind over a day) then Lithium is already pretty good and you can expect it to get bettwr as it scales out to the entire automotive industry and indeed those car batteries will be fed by the grid and can also act as short term storage and demand management.
If you cycle less regularly though, storing power for weeks or more then you need something much cheaper than lithium can ever be but if you're cheap enough you can sacrifice some conversion efficiency and still be useful in a 100% renewable grid.
This is where flow batteries are targetting, you can have a small/cheap "converter" but store the energy in tanks longer term.
But as you say, thats also basically what you can do with hydrogen/ammmonia. And as an added bonus you can buy sell hydrogen/ammonia on the open market as it's used for other purposes, which lets you insure against under/over production and take advantage of economies of scale on the converter and storage parts.
As a final bonus, during the transition you can add a percentage of hydrogen to existing gas turbines to reduce their carbon intensity and GE and other sell turbines that are built to run on gas, hydrogen/gas mixes and also pure hydrogen. This gives an easy ramp up as a carbon price and/or minimum targets can kickstart the green hydrogen industry without any particular customer needing to bear 100% of the cost.
Methane from waste can also be used as a source of hydrogen, making it carbon negative, with a promising tech looking to generate solid carbon in the form of graphite. But even if you released the carbon I to the air it's better than releasing the methane.
Low-cost methods for its safe storage and handling are well established, despite the need of being careful to avoid leaks.
Also the fuel cells using ammonia are not too different in performances compared to those using dihydrogen.
Hydrogen might be a possible choice when high energy per mass or power per mass is desired, but it is a very bad choice for the purpose of this new iron-air battery, i.e. stationary storage with very high energy capacity and very low cost.
Iron-air might indeed be the best choice for medium-time energy storage, with low cost and good full-cycle efficiency.
For very long energy storage times, e.g. years, synthetic hydrocarbons would be preferable to hydrogen, due to much easier storage and handling.
Since water is significantly more available than just about any other material, hydrogen-air cells should be the ideal battery for anything that isn't volume limited. Which is frankly a lot of cases. Unless there's some specific need for an iron-air battery where hydrogen-air can't be used, it's hard to conceive of a situation where we wouldn't use hydrogen-air.
Synthetic hydrocarbons are basically extensions of hydrogen electrochemistry. You are just adding carbon to the hydrogen made with the electrolysis step of a hydrogen-air battery. It's even possible to make a hydrocarbon-air cell such as direct-alcohol fuel cells or solid oxide fuel cells.
You are also right about synthetic hydrocarbons. The extra hydrocarbon synthesis step lowers the total efficiency, compared with using hydrogen.
Nevertheless, the lower efficiency is more than compensated by the simpler methods used for storage and handling, which require much less expensive materials and a much lower volume and total mass.
The benefits of using hydrocarbons for long-term energy storage have been amply demonstrated by the living beings that have been using this method for billions of years, many of which can easily achieve an autonomy of months without eating, while doing activities that would make a present-time robot using batteries inoperational after a few hours at most.
That might be partially true. Especially in the case of hydrogen-to-ammonia where the process of conversion is much more straightforward. However, storing hydrogen in salt caverns for years at a time is already proven. So further conversion steps might not prove any real value except where volume of storage is important.