A buried LH2 tank can have very, very good insulation. You probably want to flare off or re-liquify any boil-off, because H2 has, all told, something approaching 200x CO2's GHG potential.
Anyway, change only the assumption that hydrogen storage is free underground and watch its usage plummet into less than half. Change the country to India (that we are talking about) and see it go near zero.
Anyway, it's comparing free underground hydrogen with encapsulated portable batteries. I expect none of those to be very useful on practice.
It's supposed to be a very conservative model, with very high probability targets for costs and availability. Because of that, it's focused on public data of mature technologies. But the hydrogen industry mostly doesn't publish anything, and doesn't sell to the general population, so its numbers are all over the place.
It also ignores the equivalently closed numbers from other industries (batteries mostly), in favor of the very public values in open markets. As well as it ignores the more location dependent options, and the less consensual ones (like hydro and nuclear).
Overall, it achieves its goal very well. It's very unlikely that the reality will look like it or worse, it's almost certain it will be better.
The storage is not free, but it is extremely cheap, compared to the cost per energy capacity of batteries. Ignoring this fact will not make it go away.
Is there somebody that did a practical small scale run of this?
Hydrogen storage has a huge amount of issues that natural gas doesn't. By its face value, storing hydrogen in a natural container doesn't look viable.
There are also large scale plans in progress to do it for grid energy storage, for example in Delta, Utah. The salt formation there has enough space for 100 cavities that could, altogether, store enough hydrogen to power the average US grid electrical energy consumption for about a day.
https://model.energy/
If you use just wind/PV/batteries, the cost is almost TWICE that if you use wind/PV/batteries/hydrogen. This is for a cost optimized system relative to real historical weather data, in a solution where one is allowed to overproduce if that helps.
So, no, it's not true at all in general that it's much cheaper to deal with seasonal variations with overgeneration rather than including storage.