1. Nuclear, an up-front expensive but proven reliable way to deliver no-carbon energy at civilization scale (cf. France).
2. Renewables, which are cheap upfront, but plans for scaling them up to deliver reliable power at civilization scale are currently dinner party ideas scrawled on the back of a napkin.
It's not clear to me that we have a blowout winner here, and we should probably be hedging our bets by developing all viable options simultaneously.
Renewable technologies (including storage) that are being installed could power the world. The only question is how much they would cost, and how much costs will decline as the world invests tens of trillions of dollars in the conversion, driving the technologies down their experience curves.
Current commercially available nuclear technology, on the other hand, cannot power the world. Thermal reactors use uranium too inefficiently. Either new seawater U extraction will have to be matured (it's not ready yet), or breeder reactors will have to be matured (they are also not ready yet). Both of these would raise costs of the current nuclear system at current uranium prices.
Renewables, at least, have large and growing markets driving the learning and cost reduction, and ditto for storage. Those nuclear technologies do not.
In either case fossil fuels have to be penalized sufficiently to keep them in the ground or (and perhaps this will happen) to force CO2 capture to make them greenhouse safe too (but watch the methane leakage).
But I tell you what: in the event that this bet incredibly pans out, the downside is just that batteries cost more than we had hoped. Civilization doesn't collapse. At that point nuclear plants could be built. Is it worth building nuclear plants now that we know are going to be expensive just because batteries have a chance of being expensive?
(Also: long term storage like hydrogen doesn't need advances in batteries at all. Combustion turbines that burn hydrogen have been commercially available for years.)
And even Nasa had moved away from sorting liquid hydrogen and using it as fuel due to its crazy dangerous properties of being stored. This is not helium it effectively _eats_ the high pressure metal containing it.
And again we reach a stalemate that we would have avoided 30years ago if we had just invested in nuclear.
Nuclear is NOT perfect. No solution is. But its an excellent fit to the problems we as a species are trying to solve.
Hydrogen storage would involve compressed gas underground, not liquid hydrogen. This is a demonstrated technology. It works.
I'm not making any statement or argument to counter the fact that batteries will continue to improve a) their efficiency b) their longevity or c) their energy storage density. As you say this is a trillion dollar industry (at least).
The problem is the current state of play for _any_ ion based battery solution is that using them long term at very high scale (I'm talking national grid/infrastructure level) there are _serious_ issues they need to overcome. This isn't the same thing as building a tesla car.
By the statement of this is a demonstrated technology we should all be using nuclear batteries in our houses like the mars rover. It's a proven technology. (Incase this isn't obvious I'm being facetious).
The problems with storing compressed hydrogen isn't the long term storage in huge facilities, it's the doing something/anything with it. Transporting the hydrogen involves compressing it to liquid densities due to movement/transportation factors. A pipeline (even gas) to send this to regional burning stations would also be incredibly difficult to build/maintain due to the corrosive nature of the gas.
I'm not making an argument based the flammable/explosive nature of this, that stands for existing gas infrastructure, although this is a reason governments are looking to phase infrastructure such as this out, there are regular explosions/fires damaging houses in Europe and the UK so improving safety is a sensible concern. (Yes, albeit based on concerns that people can't do their jobs in such a way that everything is always up to spec)
With regard to efficiencies you lose several bites of the apple by taking this approach. The whole hydrogen battery chain then becomes; electrical -> stored chemical -> mechanical (via combusion) -> electrical.
I would strongly argue a gravitational battery would be more efficient (and simpler to construct) at scale for large energy storage.
i.e. electrical -> motor (pump water up into a dam) -> motor spins (via release of water from dam) -> electrical (or bricks if a dam can't be built efficiently)
And with the latter you need a hydrogen burning plant with variable capacity which is designed to be largely on standby throughout its serviceable life.
I'm not arguing against hydrogen cars, or hydrogen gas home heaters (the latter being great, thermal -> thermal for water heating is better than electrical -> thermal). I just don't see it playing a major industrial component of energy storage due to these shortcomings.