thanks for the clarification. Your right..

I guess my main point is that the laws of thermodynamics still apply, and the cost of this water to hydrogen split will cost at minimum (but actually more than) the same as the current market value of the energy market.

The catalyst I have seen quotes is aluminum which is used up in the reaction to produce aluminum oxide and the byproduct is hydrogen. In a circumstance like this, the aluminum is used up and turned into a different chemical compound which cannot be converted back into aluminum without expending the same amount of energy at minimum which was transferred to the water compound that was originally split up.

so in actuality, the water is not the only fuel. As long as you have water you still don't get hydrogen. You have to have water plus some other compound which is splitting the water into hydrogen and oxygen. and that chemical (whether aluminum, or otherwise) will have to be produced in a factory which will cost the same amount of energy the car uses driving down the road.

So call that a catalyst or call it something else, the energy cost will still come from a coal or fission burning factory, which have arguably worse cost and environmental impact then direct burning of gasoline.