In addition to that, hydrogen can also be used differently, namely in internal combustion engines that use the Otto cycle — e.g. spark-ignition engines, like a petrol/gasoline engine. Refilling the tank uses the same procedure as with a hydrogen-electric vehicle, and what comes out of the exhaust will be the same as well, but possibly added with a mild percentage of lubricants, given that it's a piston engine.
So hydrogen is actually a dual-purpose fuel — or rather technically, not a fuel but an energy carrier — and it would solve many of the existing problems. However, the problem is political willingness. The infrastructure for the distribution of hydrogen just isn't there yet, and considering the risk of fire and/or explosion — hydrogen can readily be combined with oxygen and other airborne gases in the presence of a spark or a flame — the political-industrial apparatus rather places its bets on battery-electric cars and plug-in hybrids that have limited range, with heavy and expensive batteries with a limited lifetime, which need over an hour to recharge on a speed charger — or about 12 to 14 hours on a domestic power outlet — and that don't perform very well when it's freezing outside.
Harry Metcalfe has tested many battery-electric and plug-in hybrid cars on his channel, and the invariable conclusion is that they can only get about half the range that the manufacturer claims they would.
One reason for this is that the manufacturer-claimed range can only be attained with extensive use of regenerative braking — the car's brake system incorporates a generator that feeds electricity back into the battery — which works well in stop-and-go traffic or with a sporty driving style that involves many corners, but it is completely useless when you're cruising on the highway, because then you won't be using the brakes all that much. And in winter, the car's effective range drops to about 60%, because the batteries don't perform well when it's freezing — a phenomenon also already known from using cellphones and smartphones outside in winter.