I think they really just do it because generally everything you will connect to the battery, for the most part, will be using the same voltage, and it’s just easier to do your math and in your head. Remember, most people can’t just calculate a 20% tip in their head without having to think about it for a while or use an app.
Also, in this particular instance, phone batteries are measured in miliamp hours, so it makes the thing I actually want to know, how many times can it charge my cell phone, really easy to figure out.
But as somebody who tinkers with inverters and such, I agree, it is annoying. It is still generally not that hard to do in my head, and trivial with a calculator. But I’m with you.
That's wrong, if they only specifiy Ah, then they usually imply cell voltage (3.7V avg.) and not the 5V you're drawing over USB.
Even if you assume you're charging a phone with that, you first need to subtract 25-40% total losses. And then consider that phone batteries are LiHV with 3.85-3.9V nowadays.
Well, and if you are on that train: instead of Wh, why not use J?
(Though for American hikers it would be somewhat fun to use a unit of 'pound feet'.)