It seems that the Sabatier reaction solves the biggest problem of climate change — it does create clean gas and hydrogen fuel from the captured carbon dioxide and water (from melting ice).
$$\ce{CO2 + 4H2 -> CH4 + 2H2O}$$
Currently, there is temporal overproduction of clean energy and problems with its storage. E.g., some countries (in Eastern Europe) have stopped support for new solar panel parts because the current electricity systems cannot cope with the overproduction of solar electricity, especially during the spikes. Why is there no industrial deployment of this reaction?
I can imagine several challenges that can be too difficult to overcome:
$\ce{CO2}$ is plentiful but there may be no process to capture it from the air and such sucking can have a bad impact on local regions (all the $\ce{CO2}$ is sucked from some region and there is no sufficient amount left for plants and crops)
The reaction requires $3\,\pu{MPa}$ pressure and it may be impossible to achieve such high pressure.
The reaction requires some catalysts. While $\ce{Ni}$ is mentioned, it itself is costly and may require replacement with costly rare earth catalysts.
I have no idea about all of this. But the idea seems to miraculous not to think about it.
There is already a more general question that was asked 10 years ago. My question is more specific and the situation has changed. Especially - my question exclude the energy as challenge. While the cost of energy can be high (e.g., in NordPool 2022), generally there are solar panel solutions that are not being adapted because of the energy storage and flow unreliability problem. So, the cost of energy stems mostly from the problem of storage and not from the global availability of electricity. As I said, some countries have withdrawn support for solar panels and explicitly states that no new solar panels can be connected to the grid. So, the energy challenge should be considered as solved in case of my question.
Note added: while the energy storage is an important point and application of methane production, my question is concerned about methane production proper. We can and we should abandon the fossil fuels but - as I understand - methane is used as important input in other chemical processes and manufacturing (non-energy use, especially in Germany) and that is why it may be required to produce it because of its own merit. It is though, interesting, that the wiki page of non-energy of methane https://en.wikipedia.org/wiki/Methane#Chemical_feedstock does not give any valuable information. It gives many hints how methane is used for the production of H2 which is used further for the fertilizers, but such use of methane can be replaced by other input and that is why methane can be avoided in that use as well. But in any case - I guess that there may be chemical processes which require methane without alternatives and that is why methane production can be beneficial.