The problem is that in gas form hydrogen and oxygen take up more volume than they would as liquid water. To store them compactly you have to cool them to liquid, but that requires a bulky and power-hungry refrigeration system.

Also, hydrogen is a nasty thing to try to store in pure form. You have to deal with embrittlement. Hydrogen has one electron which it easily gives up to form a chemical bond with whatever happens to be around... such as the walls of the storage vessel or the seal around the valve or whatever the valve is made of... and that bond degrades the integrity of the container and eventually it leaks, and then you have a pure hydrogen leak to deal with. Most applications that need hydrogen try to generate it as close to the time of use as possible. Trying to keep pure hydrogen in a tank sucks.

Hydrogen + oxygen is the most energetic chemical reaction you can get, which makes it effective for rocket propulsion. But there are other fuels used such as RP-1 (refined kerosene) because they're less of a PITA to deal with than hydrogen and depending on your rocket design you might get better efficiency if you don't have to carry the extra weight of the hydrogen cooling and storage system.