If you can mine blocks for free, the value of each block plummets.
There's a hundred other things we can dump energy on before deciding to waste it ; pumping water uphill, gravity batteries, regular batteries, electrolyzing hydrogen to use for later, ...
Fuel, "Storage", Ammonia etc
Hydrogen is likely to become the default go to once we start hitting these "fee energy" zones in big enough numbers.
If energy is expensive than it's makes more sense to store it in batteries than hydrogen since batteries are about 3X as efficient as the hydrogen cycle.
If energy is cheap it makes more sense to use about twice as much energy to capture and attach carbon molecules to that hydrogen to create a hydrocarbon resulting in something that's easy to store and transport, and that uses existing infrastructure.
If we follow your 3rd paragraph and turn the hydrogen into hydrocarbons, not only do you lose efficiency in that process, you make CO2 as a byproduct of combustion again
Nobody is interested in storage that turns your carbon-free green energy back into greenhousing energy
The reason you might want hydrogen instead of batteries is just cost, I guess.
If you make your hydro-carbons with captured carbon, the process is slightly carbon-negative. ~10% of hydrocarbons are not burned, they're turned into plastic or lubricants etc. So for every 10 carbons you take from the air, only 9 are released back.