And that's the issue, no different than hydrogen: we can do that, but in sooooo limited quantity that's practically useless.

I'm not sure why you would think the quantities of hydrogen that can be stored are a limit in practice. Certainly we can store at least as much hydrogen in the form of methane as we have ever extracted natural gas from natural gas wells, which is decades' worth of consumption, not a mere 40 hours' worth.

Maybe I was not clear: the quantity of green hydrogen we can produce is negligible because the amount of energy needed to extract it is so high, the amount of energy needed to compress it in a tank, respect of the rate of usage in a fuel cell makes the balance ridiculous: you need a hectare of p.v. to produce few grams per day of hydrogen or you need a good sunny day to produce enough for a mile or two in a fuel-cell powered car. At that point the entire "economy" is just marketing.

Oh, that makes sense! You're coming to ridiculously wrong conclusions because you're working from ridiculously wrong data, but not about the storability of hydrogen; rather, about the relevant efficiency figures.

Let's put some concrete numbers on this. Grid-scale PV in California has a capacity factor of 29%, based on a nominal efficiency of typically 21% and a nominal solar constant of 1000 W/m². This gives 61 W/m² of solar cell as a round-the-clock average. A hectare of solar cells would be 10000 m², but because solar cells are more expensive than land they are not placed edge-to-edge without gaps; I'll guess that 30%, 3000 m², is a closer estimate, but I'd appreciate better figures from real utility-scale PV installations. That's 180 kW per hectare, round-the-clock average.

Hydrogen has a LHV of 120 MJ/kg, so with 100% electrolysis efficiency 180 kW would work out to 131 kg per day per hectare, using the 30% fill factor above. Actual electrolysis efficiency is only about 70% in current industrial practice, reducing this to 92 kg per day: https://en.wikipedia.org/wiki/Electrolysis_of_water#Efficien...

Then we have the question of how much energy is lost in compressing the hydrogen for storage. This is a little tricky to calculate because the answer can be arbitrarily low (isothermal compression is perfectly efficient) and even adiabatic compression depends on the kind of gas you're compressing, but the electrolysis link above says, "Practical electrolysis (using a rotating electrolyser at 15 bar pressure) may consume 50 kW⋅h/kg (180 MJ/kg), and a further 15 kW⋅h (54 MJ) if the hydrogen is compressed for use in hydrogen cars.[37]."

So we're at 234 MJ/kg in, 120 MJ/kg out. This gives 67 kg/day of hydrogen for our hectare. This is an average including the occasional cloudy day that happens in southeastern California; on sunny days the number is higher.

67000 grams is, I think, not accurately described as "a few grams".

https://www.fueleconomy.gov/feg/fcv_sbs.shtml says current fuel-cell cars on sale in the US go 64–72 miles per kg, or, in non-medieval units, 103–116 km/kg. 67 kg (again, an average day, not a sunny day) thus gives you 4300–4800 miles, or, in non-medieval units, 6900–7800 km.

6900–7800 km is, I think, not accurately described as "a mile or two"; even though there are admittedly many different incompatible definitions of a "mile", none of them is close to 1000 km long.

In extremely polar countries like Germany and the Netherlands, PV capacity factors are much lower, sometimes below 10%, so you have to divide all these numbers by a factor of about 3.

So, how did you end up believing figures that were wrong by three or four orders of magnitude, and with such confidence that you were dismissing correct, factual accounts of energy economics as "just marketing"? And how can you avoid getting suckered into such swaggering delusions in the future?