This assumes you have a nice handy place in the hills to build a reservoir along with a source of water. Most of the good sites have already been taken, and you still run into the problem of scale. Largest pumped hydro project in the world is about 24GWh storage and 3GW generating capacity, which doesn't even come close to keeping the lights on in my city.
Everything associated with hydrogen is a pain in the ass. Any kind of storage is going to be far more difficult & expensive than natural gas, same thing with transporting it around. Producing it also takes a ton of energy so combined with the storage & transportation issues and it's always going to be really expensive and a PITA to work with. IMO hydrogen is just stupid unless we have so much nuclear power that it's too cheap to meter, save it for stuff like rocket fuel where it really does make a difference.
Fun fact I worked out on the back of a napkin a while back. If we magically turned every car in the US into a hydrogen powered vehicle, it would take almost twice as much energy to keep them running compared to using gasoline. You'd have to burn twice as much fuel in the power plants to generate the electricity for making & distributing hydrogen compared to simply burning the fuel in the car engine. Unless you're in France or BC where almost all the electricity comes from nuclear or hydropower, you'll end up polluting MORE if you tried to run the transportation system on hydrogen.