Its also logistically hard to actually get the energy back into the grid from cars. Driving around with it is fine but if you cant put the energy back into the grid at peak time you still have to over produce more energy in total than just to cover the peak. It uses the energy which is good but it does not reduce the difference between peak demand an low demand. If that is reduced it has an overall larger impact than just to using the excess energy.
Pumping water back up into a reservoir is the most common and probably oldest way to store excess grid capacity like an actual grid batter (one that gives energy back to the grid). Ofc its not feasible in many places due to the lack of hydro power plant but there are other ways to actually store energy and deliver it back to the grid unlike the Buttcoin battery nonsense.
With water, you tend to use the cheapest option. If you are in the middle east on the coast, far from rivers or other sources of drinking water, desalinating is pretty much the only option. Which is why that has been common for decades. With green hydrogen, what matters is the cost relative to hydrogen produced from natural gas. Both are dominated by the variable cost of the energy rather than construction cost.
Bitcoin as a green, or rather less hopelessly planet destroying thing, does not make sense because it removes energy that could be used for actually doing something more worthwhile.
We need more solutions that work like pumping water back up into a reservoir (see other reply). These solutions aren't at risk that they need to run on high energy cost anyway to stay profitable.
Desalination plants aren't really something you build for profit, they're to secure your cities clean water supply and are usually taxpayer funded infrastructure projects.
A realistic/feasible deployment would perhaps pair desalination with solar or wind (more likely on the coast). During electricity peak hours, it might be more lucrative to sell electricity to the grid and then the rest of the time top up the reservoir. I guess depending on how scarce water is, the $ per kwh earned via water might actually be larger than selling to the grid. But you get my point.
You are right that these things being funded via tax payer money, makes this kind of lateral thinking less likely. But if someone were to do this commercially, this would be a great way to make it more cost effective.
So those are good uses of off-peak power when your local economy is already interested in having those things. The state also has some other initiatives to use the excess generation, such as residential water heating and EV charging using "smart grid" sockets that take into account the local and greater network's load and generation.
Ideally you need something where the cost of electricity would normally dominate the capital costs of setting up the operation. Otherwise, you're better off running the process all the time, and it's not a useful grid battery.
Alternatively, something where you need to overbuild the infrastructure, perhaps to serve peak demand or for emergency availability.
Water desalination plants and hydrogen factories are expensive to build, so they don't work well here. Bitcoin mining rigs aren't free either. Charging cars is a great application even though cars are expensive to build: they meet the second criterion as, for logistic reasons, we build way more cars than are on the road at any point in time.