I agree that at current CapEx you could never run a plant 1/3 of the time and make it look good but I think this ignore two things:
1) If you take net zero as a hard goal, i.e. not one that is subject to economic tests except in relative terms then hydrogen as large scale energy storage only has to beat alternative technologies, regardless of how expensive it is.
Battery storage will absolutely dominate intra-day balancing and hydrogen will have no role to play there but the high cost per unit of energy stored of a battery doesn't work for inter-seasonal or for dealing with an unusually high demand year. (in a European context, a very cold winter for instance). No, future cost reductions will not solve that for the simple reason that the capital cost of a unit of battery capacity has to be recovered over its cycles. So a battery that cycles once a year incurs 365x the capital cost per cycle that one which cycles once a day does. In many renewable dominated power markets, current battery tech is competitive in the intra-day market. To be equally competitive in the seasonal market, you'd need two orders of magnitude cost reduction which doesn't seem possible on materials cost grounds alone. I don't see how iron-air and other battery chemistries stack up here either and to be honest, if we're going to compare long term energy storage technologies on a level playing field we have to compare like with like. We can't say "batteries" are getting much better and cheaper and are proven technology compared to hydrogen storage and then it turns out that the batteries in question are early stage VC projects.
When I look at the trajectory of grid scale battery storage vs hydrogen, I see a battery technology developing that will completely own the intra-day and probably the intra-week world but that has no chance of dealing with seasonal peaks.
Europe is prone to extended periods of cold, overcast, and windless weather which lasts for weeks and stretches from Ireland to the practically the Urals. That is the system stress condition and no system that cannot handle it can be said to be functional. The same might not be true everywhere, solar has less variation than wind and maybe California doesn't need seasonal storage, I don't know, but this is at least one area of the world which does and I suspect there are more.
Ideas which involve very long distance electricity transmission simply will not work for geopolitical reasons. If anyone fantasised about it before February of this year, they can now forget about it. No doubt electricity will be moved substantial distances but no government will allow the ability of its citizens to have winter heating / summer cooling to depend instantaneously on governments it cannot trust. Short distance integration of the kind we see in Western Europe, sure, but that doesn't really help because there's a lot of temperature, wind and insolation correlation between those countries anyway.
So hydrogen storage is lossy but the alternatives don't make the models stack up, except for a massive wave of nuclear new-build. I don't know which will be cheaper but these are both not cheap options. Proposed alternatives have to pass the test of dealing with this seasonal (and multi-year scale issue)
2) If you look at where power generation is going in high renewables markets, it is clear that we will soon have a situation where for many thousands of hours a year, we have deeply oversupplied instantaneous demand. That will be true even after intra-day load shifting, EV charging etc. This is in fact efficient since the cost of undersupply is asymmetric and vastly higher than the economic cost of oversupply. The system will be net long for most of the year and net short for a much smaller number of hours, during which period the value of dispatchable energy will be very high. More overbuilding shortens the net-short period but creates much more energy over-generated over the course of the year.
That means that your capital intensive electrolyser plant can run at full capacity the majority of the time, reduced capacity occasionally, and has to be off maybe 10% to 20% of the time. That is much easier to make work than 33%.
(I am assuming only modest electrolyser cost reductions)
The issues I have with a lot of analysis of hydrogen is that people do a quick order of magnitude comparison to either fossil gas or to batteries in the intra-day world and say, "why would you do this?" as a rhetorical question when they should be noting that fossil gas isn't a long term option, batteries aren't playing in the more than a day market at all (since there is currently no reason for such a thing to exist) and asking the question seriously rather than rhetorically.
People have been spoiled by the easy energy transition successes so far, moderately deep penetration of wind and solar into electricity and EVs and they expect that the whole energy transition will be delivered by technologies that compare favourably even without costing carbon emissions with the fossil fuels they displace and the reality is that we are not owed a set of technologies that are cheaper than fossil fuels.