Storing energy chemically is very, very energy-dense and efficient. A rechargeable battery has to carry all its reagents in a sealed canister, and it has to have a fully reversible cell chemistry, which makes for relatively poorer energy density and a great deal of design complexity. A hydrogen-fueled vehicle only needs to carry fuel; the oxidizer is in the air all around (yes, I realize atmospheric source of O2 isn't good for fuel cells, but it's fine for H2-based internal combustion engines). What's wrong with a gas-station-style distribution network, by the way? No different from a charging station network, and a gas station style distribution involves a great deal less energy loss due to line resistance for electrical distribution. Hydrogen, unlike (say) methane or petroleum, can be piped around with little or no fear of what happens if the pipe is ruptured - at worst, it's a fire hazard, but it's not an environmental hazard because the leaking gas will rise and disperse.
Sure, the energy equation for extracting hydrogen isn't awesome (though I suspect if you ACTUALLY boil down ALL the inefficiencies in the electric-car-based-on-LiIon-batteries equation, the actual "joules in to miles traveled" ratio likely favors hydrogen by a long shot). But who cares if the source is, for example, solar, wave, hydro or wind energy from a station close to the sea, which also happens to be a great source of non-potable (therefore not competing with human drinking needs) water?