LP, The efficiency of the engine was just a wild guess to make a point..it could be less or more.

Yes, from the environmental perspective it apparently makes sense but to split the water one needs energy from another fuel or any renewable source. If someone can use solar energy to split water, then solar cars would be more efficient theoritically and we wouldn't need water at all.

Or find a more stable compound of hydrogen than water to get higher energy levels at the ignition point.