The historical and most currently developed production of H2...

The historical and most currently developed production of H2 generally occurs adjacent to its end use in probably 90% of cases. Its expensive to transport because of its extremely low density. It either needs to be heavily compressed, or it needs liquefying. In some cases converted to a transition liquid such as ammonia or MCH as some are trying.

Those both have a thermodynamicaly based cost in and out as well.

And yes, the absolute inefficiency and cost of producing green hydrogen through electrolysis adds even more to those costs overall. Astonishingly energy intensive for a comparatively low energy 'output' or 'storage' in H2. It's really only beneficial as a chemical feedstock in cases where there isn't anything else you can use, it is vital in a number of processes. None of which have ever been as an energy vector as far a I am aware, besides rockets firing into outer space.