@Laidback:
For Wh being common we have to blame Bosch and Shimano etc.
I think it predates that, back to when energy companies switched from British Thermal Units to kWh. At least BTUs didn't have such an easily confused abbreviation, though very few people knew how much energy a BTU actually was e.g. in terms of Joules (It's actually a bit more than 1kJ, to a rough approximation). Probably all because of that pesky Common Market, as it was in those days.
I bought an LED replacement for an ageing fluorescent tube today. It is F rated for energy efficiency (the ratings go from A upwards through the alphabet these days, i.e. the reverse of what they were until quite recently). I looked on the packaging for the actual wattage of the thing and finally found "22kWh per 1000 hours" - in other words, 22W. Beats me why they couldn't just have said that. Still, it's a lot better than the old 68W tube it replaced.
Danish company Promovec rate batteries in Amp Hours Ah. Then we have to multiply the voltage x Ah for watt hour equivalent.
Ah works OK-ish for single cells such as AA NiMHs and the pretty common 18650 rechargeable Lithium cells, because you know the voltage of the cell - it's defined by the chemistry. I can well see that it would be a pain for packaged batteries* because you don't necessarily know how many cells are inside (though you could probably make an educated guess).
* Back in my school days I was taught that a battery consists of multiple electrochemical cells. However, in reality more or less everyone calls anything with a + and - terminal on it a battery, even though many common batteries such as the AA and AAA are actually single cells. (I think Wikipedia fudges the issue somewhat by saying that a battery consists of "one or more electrical cells"...)