> why not cut out the middle man?

Because batteries are somewhat bigger and heavier than hydrogen fuel tanks for a given amount of energy. Or to put it another way: For the same weight and size, a hydrogen vehicle will have a somewhat greater range. That's why hydrogen's being suggested for long-distance transport (trolley buses already use overhead power lines).

.... Hm: that might not be the case if the vehicle also had to carry the oxygen for combustion, rather than breathing air, in order to eliminate the NOx emissions.

.... Hm squared: bubble the engine output through water, and you've not only got a catalytic-converter equivalent, but you can also siphon off the NOx at the fuel depot, and use it as feedstock for producing fertiliser. I'm sure one of the big boys has already patented that.