Regarding energy density - definitely agree, my own research showed me a 2 fold increase in consumption compared to LPG, which in turn increases consumption by 15% over regular petrol (note that these were estimates based on my data).
The lab had a "Hydrogen maker" - obviously it ran off electricity and in about 6 hours provided roughly 500 milliliters of compressed hydrogen (kept at 350 bar if I remember correctly) literally from air.
My concept was to be able to have a clean water tank (pure H2O) and electrolysis providing the Hydrogen to run the engine, and continue on in a closed loop; literally a car running on water. Obviously energy transfer, efficiencies etc make this almost impossible - but one can dream.