(My own disclaimer: I am researcher in hydrogen & fuel cells)
Containing hydrogen is no longer much of a problem, though compressing it in the first place is still expensive. Still, you don't really need a distribution network: the trend is to use electrolysers and produce the hydrogen locally. With the increased share of non-programmable renewables like wind and solar, hydrogen stations can produce their hydrogen when there is an excess of available power.
It's not just the price of batteries, which may very well come down: it's their weight. There is only so much that can be done now to increase Li-ion energy density; Elon Musk was dreaming of using graphene for superbatteries, but that's a very long shot. Sure, hydrogen cannot compete in the short range with batteries, but it is much better in the long range. And yes, batteries are much heavier than the tanks containing hydrogen.
The energy density of Li-ion batteries is about 100 Wh/kg, hydrogen is 32500 Wh/kg. Even accounting for 50% conversion efficiency and a hydrogen tank 10 times as heavy as the hydrogen, you still get over 1600 Wh/kg, well over 15 times Li-ion! Then of course you need to add the fuel cell system, which is dimensioned by power (not by energy as the tank is), and its weight is why FC cars are better in the long range, where this weight is a smaller fraction of the total FC system weight.
Running fuel cells on hydrocarbons directly is not an option (slow chemistry), but they can be reformed on-the-fly to hydrogen; in fact you can do that with diesel. The only problem is, the system gets so much complicated it is soon not worth the bother when you have a highly dynamic load as is the case for a car.