Comment Could be worse. How about BTU? (Score 1) 51
British Thermal Unit doesn't give any hint at all...
I suspect starting with power (vs. energy) is historical. It's horsepower, not oats/second.
But really, which unit is most natural depends on what you're engineering. If you're making a transmission line or a motor or a heater, power is what matters. With a car or a train, power is what gets you over the hill. And you don't buy fuel by the MJ, you buy it by the liter (or, gallon in Freedom Units).
Even just with electricity, storage as electricity is a relatively new thing outside of niche cases like battery backups for telephone substations (you know, back when it was 42V over a copper pair to your house). If you needed to store power, you did it as fuel for a generator. And then that has to take into account the efficiency of the generator.