Hydrogen can be produced from nuclear, as well as hydro power. If produced in off-peak times (at late night) in bulk it can be efficiently produced and then distributed to filling stations. With at-home production units the distribution system can be largely removed at the expense of slightly higher per unit cost and less efficiency than bulk.
Synthetic petroleum is produced from coal, oil and natural gas, carbon energy sources that don't help reduce environmental footprint.
You can make gasoline out of nuclear power, too, from atmospheric carbon dioxide.
Last I looked, a hydrogen fuel cycle was slightly more efficient than a gasoline fuel cycle. But it's a lot easier to handle gasoline than hydrogen. We already have the equipment to move and store gasoline all over the country, no cryogenics needed.
(I say "gasoline" but things like methanol are also suitable.)
Wouldn't those sources of gasoline from atmospheric carbon dioxide still produce carbon emissions? While hydrogen used as a transportation fuel produces water.
Synthetic petroleum is produced from coal, oil and natural gas, carbon energy sources that don't help reduce environmental footprint.