Storing methane is cheaper, and you can use it for heating, it brings down costs when used in addition to hydrogen storage:

https://arxiv.org/pdf/1801.05290.pdf

" 4.7. Methanation scenario - In the Methanation scenario the conversion of hydrogen to methane is allowed, which can then be fed into the natural gas network for use both in the heating and electricity sectors. Since the carbon dioxide required for the methanation is captured from the air, the methanation has a low overall efficiency (60%), but the resulting methane is extremely valuable to meet the peak heating demand.Despite the costs of the methanation equipment, total system costs reduce by 11% compared to the Heating scenario. In the heating sector, a substitution of heat pumps with gas heating can be observed in Figure 9. Significantly reduced CO2pricesand average marginal prices for electricity and heating are also seen in Table 3. Furthermore, the benefit of transmission reinforcement is weakened, since the methanation allows the use of cheap gas storage to smooth synoptic and seasonal variations of renewables. Optimal transmission reduces the total systems costs by only 17%, compared to 25% in the Heating scenario,and the optimal transmission volume is also lower. The total volume of synthetic methane produced with no transmission is 708 TWhth, compared to 795 TWhth from natural gas. With optimal transmission the volume of synthetic methane reduces to 263 TWhth as transmission smoothes more synoptic variations of wind."

Hydrogen is really hard to store, though.

EDIT: should have qualified my statement with "in man-made objects"

No, actually it's pretty easy, in underground caverns (cheapest is solution mined cavities in salt; cost per kWh of capacity about 1/200th the per-energy cost of batteries.)

Interesting