The only advantage of hydrogen is that contrary to electricity, you can't easily produce and store it by yourself, and thus is more easily taxable. Also, because all the infrastructure need to be created from scratch, there is no big player yet and there is potential to make a lot of money.
A lot of the infrastructure isn't there, but there for sure are big players - most of currently available hydrogen is made as natural gas and oil byproduct, so oil and gas companies have a lot of it.
Selling hydrogen as green is a way for them to stay relevant.
Hydrogen is so incredibly easy to make yourself that I bet the ancient Greeks managed it by accident without knowing what they'd done.
This is in part because the actual scientific production of it via electrolysis predates batteries and dynamos, and instead involved generating electricity by rubbing things together, and the ancient Greeks doing this is why electricity is named after their word for amber.
Personally, I made it myself at single-digit-years-old with a battery, some wire, two pencils, two jam jars, and two yoghurt pots to stand the jam jars on.
Making hydrogen storage systems might not be a DIY option, but making the stuff itself certainly is.
The only single reason that I won't "produce significant amount of hydrogen to do anything" is because I don't need to.
It's already available in convenient and practical forms for people who do have a use for the stuff, and production is sufficiently efficient for it to not be an obviously bad idea for energy storage.
