If the batteries themselves were to remain expensive even as the electricity to charge them/electrolyse water became cheap, I can imagine a scenario where the lifetime cost difference between batteries and hydrogen tanks might be more than the cost of the energy wasted as heat by making the hydrogen. I don’t think this will happen now.
The same dynamic on a slightly smaller scale means I can also believe that hydrogen cars could be a Vimes’ Boot: low purchase cost, high running cost, so poor people have them because they can’t afford the cheaper option.
https://en.wikipedia.org/wiki/Electrolysis_of_water#Efficien...
Not that this changes the picture of hydrogen powered personal vehicles. Still the only viable option for grid level seasonal storage.
Liquified ammonia will also be popular.
But we don't need any seasonal storage at all, just as we don't have seasonal storage of oil. We only need enough storage to hold out until a shipment of LH2 or LNH3 arrives from the tropics.
Efficiency of H2 needs to fold in the cost of getting the power back out: Cf. "round-trip efficiency". But as I said, it doesn't matter very much, anymore, since generation is getting so cheap. Gasoline engines were never efficient, but few have cared much about that.
Hydrogen won't, in any case, be "transported to the fuel station". It will be made right on the spot, or just down the street. And, won't be compressed, but will be poured in and allowed to boil up to pressure.
That said, cars will be using batteries for the foreseeable future. In 20 years, H2 might get another chance, if batteries don't improve enough. Which seems unlikely.
Are the efficient machines you are talking about affordable and portable enough to be locally owned?
Also you are talking about hydrogen being poured in - so that would be cryogenic cooling, right? that incurrs an energy cost as well?
But by the time we are doing that on every street corner, the whole grid will be driven from renewables, and joules will be very cheap vs. other concerns. In particular, the LH2 will be banked during peak generation time, so almost free.
Likewise, nukes: a dollar plowed into nukes generates, many years later, much less power than a dollar of renewables that start producing immediately. You spend on coal the whole time while the nuke is being built, and the amount you have spent just on coal, by then, would have bought as much renewable generating capacity as your nuke.