This is an important question. The key point is that water is not fuel
. It's already in its low free energy state. Hydrogen +oxygen is fuel, since it's in a high free-energy state, but unfortunately, as you say, it's hard to carry the hydrogen around.The energy to electrolyze the water has to come from somewhere. That means you still have to carry around some energy either as gasoline, charged batteries, or some other form. Using that energy to electrolyze water and then burning the hydrogen only wastes some of the energy, since neither step is 100% efficient.
Can there be any point then to having water and electrolysis on a vehicle? Maybe. Standard vehicles use batteries, since there are lots of ways that specifically electrical power is useful. They charge those batteries with energy from the standard fuel. That's not 100% efficient but it's an important part of a modern vehicle. It's possible that a water fuel cell could be developed which might effectively replace the battery with a lighter device.
That would be particularly important in hybrids and all-electric vehicles, where the battery is currently used to store a major fraction or even all of the free-energy. A lighter, smaller replacement for the battery would be a big deal. Of course, the energy even in an all-electric vehicle doesn't ultimately come from the battery or fuel cell. It comes from a power plant that burns coal, or uses nuclear fission, or a hydroelectric plant, or a solar panel, or a wind turbine, etc.
p.s. I found that old cycle article. It just says that "When the hydrogen boost is active, gasoline consumption is reduced by 50%." Of course, when the boost is not active, gasoline consumption is increased
to provide the energy to electrolyze the water.
(published on 01/31/2011)