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Vehicles
We already have these. Electric motors are exactly what we need. With a fancy fuel cell stack, hydrogen is converted into electricity. The fuel cell stack does have a byproduct; water vapor.
I think what you are describing is a vehicle like the Chevy Volt, but with the gasoline-powered generator being replaced by hydrogen. It could be an effective solution, though it is not necessarily the best solution.
Combustion energy conversion ratios are lower than PEM fuel cell stacks.
Rather than focusing on hydrogen, I think a more realistic option would be to stop at an intermediary step proposed in your OP.
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If we are generating the power needed to create the hydrogen gas in a green fashion, and the only perk to using hydrogen is that we can transport the energy, I'd propose focusing on improving battery technology, or ideally making the switch over to capacitors once we can figure out how to increase their capacities.
It'd be nice to skip the intermediary step, but we just simply can't for portable energy.
Battery technology has improved a lot over the past couple of decades, but fuel cell systems have become way more cost effective. Storage of hydrogen at high pressures is less resource intensive than holding the same power in lion-ion batteries (even with losses included).
Also, tanks have way more cycles than lion-ion batteries, and the durability of fuel cell stacks are insane.