It would make the discerning consumers life a bit easier maybe. Situations like you link to could certainly be avoided.
However when comparing batteries I wouldn't say watt hours is "correct" more than I was say amp hours without considering voltage is incorrect.
Watt-hours is a unit of energy and is better for the laymen to compare different but somewhat similar batteries because its calculated with nominal/average volts already considered. Its also easy to grasp as a concept because its watts per hour...easy enough. However using an average voltage (since voltage drops with usage) will get you an average watt hour.
Amp hours is a unit of charge and can be confusing because its amps * hours giving what appears to be an arbitrary number if someone considers it like watt hour. Its otherwise shorthand for obtaining coulombs (1 amp = 1 coulomb per second or 3600/hour, 1 coulomb is 6.xxx * 10^18 electron charge). Although I'm not an engineer I believe this is just a faster method for engineers to calculate battery requirements based on specific applications current draw requirements.
The capacity of battery will be affected by a lot of variables too. Temp, discharge rate, depth of discharge, cycles, manufacturer derating the battery, and of course what you are doing on the device as typically the higher the current draw the lower the batteries overall capacity is becomes for that cycle.
In the end I believe mAh is just a method to get to the actual goal of the engineer, battery life quantified as an amount of time. The average customer doesn't care about watts, amps, etc nor do will they be comparing their laptop to their smart watch or flashlight to their camera. They just want to know if their new smart phone will last longer than their old one.
