That's how un-scalable long-term battery storage is. Hydrogen is more so: you can store hydrogen in vast quantities in salt caverns, and move it around. Pumped hydro is best, but sites are limited. Compressed air is another solid contender.
Turns out that pumping water up-hill and running generators when the water flows backwards is a very efficient energy storage mechanism.
Do you mean 10% of the generation on a typical summer day? Or 10% of the generation of an entire summer?
The problem with this kind of calculation is that battery technology (and cost) is very much a moving target.
LFP would probably be the better choice today. It's cheaper, safer, and can handle far more load cycles. That comes at a cost of a lower energy density, but that hardly matters for utility scale batteries. Tesla's megapacks use LFP already - https://cleantechnica.com/2021/05/11/tesla-transitions-to-lf....
Like you say, there are many other energy storage options like pumped hydro, compressed air, etc. My personal favorite is the train full of concrete that goes up and down a hill (https://interestingengineering.com/concrete-gravity-trains-m...).
My opinion is that we need a mix of energy sources and we need a mix of energy storage solutions.
Falling battery prices helps of course but we are very far from a point where we can eliminate the need for hydrogen.
A 10k km HVDC line is enough to draw power from places 90 degrees apart in terms of latitude. Similarly, between the east and west coast of the US there's around 3h of a time difference.
Chile is planning on building an even longer cable, so it's entirely in the realm of possibility:
https://www.pv-magazine.com/2021/11/15/chile-wants-to-export...
I imagine the cost of hydrogen storage is significantly less than batteries, thereby offsetting the reduced efficiency of turning solar power into electricity. The main issue we have with solar is storage for when the sun isn't out.
This is about splitting water using electricity. You can create and use the fuel at the same site. Just need a water pipe and a connection to the grid. Splitting off hydrogen at a separate site is just wastefull.
My point is create an energy storage station, all you need is water and grid power. No pipelines needed. This hypothetical power storage site would generate hydrogen during the daytime from surplus grid solar, then burn the hydrogen at night delivering the power back to the grid.
To be clear, I'm not necessarily talking about a solution for homeowners. An energy storage facility could cheerfully be as large Diablo Canyon Power Station. It just depends on the efficiencies of everything from the water-splitting process, storage solution, grid losses, and grid capacity.