Why do (kilo)watt-hours double-count units per time? A watt is defined as 1 joule per second and is therefore a measurement of energy transfer over a period of time.
A kilowatt-hour is a measurement of energy equal to one kilowatt sustained over a period of one hour.
What is the point in double counting units per time? It seems to me that a kilowatt-hour could be more simply expressed as 3.6 megajoules.
This question was prompted by this article which triple-counted the time unit (using seconds, hours, and days): "New York City [uses] about 12 gigawatt-hours of electricity a day" Would it not be simpler and more intuitive to just state: "New York City uses 43.2 terajoules per day" or "New York City uses 500 megawatts"?
Is there a justification for using kilowatt-hours or is it used for historical reasons?
 A: Practically speaking, maybe you want to know how much energy it takes to keep your refrigerator running for one hour. On the back of a fridge you can find the power in watts. If you measure energy in units of $kW\cdot h$, it's easier to figure out how long you can keep it running.
You can call it the "natural unit for a thrifty man".
A: The way you phrase the question is slightly ambiguous, it doesn't double count units per time. One is per time, the other is $\times$ time. And therefore cancels to get joules. However just using joules, you get no idea on the time period that amount of energy was used, just the amount. Using $kW\cdot h$ gives you a reference for how long you used an amount of power for. Joules has no real practical meaning to the lay-man whereas all appliances are in Watts, because you need to know how much energy an appliance uses in a specific time ($1s$). You can't have appliance ratings in joules that makes no sense. 
A: There is historical reason behind using kWh as well as matter of general convenience. Many people around the world pay their electricity bills using the "per unit of electricity" concept that energy provider companies have defined as 1kWh.
Generally, the supplier has a base charge/connection charge for a certain number of electricity units (say "$b$"). Any usage above $b$ would be charged extra based on different price brackets. As you mentioned NYC in your question, here is an example [2] :

Now, why Wh or kWh is used here? It is because the general consumer has an easy way of verifying how much electricity they have been using by simple multiplication. All electrical appliances come with a power rating in W or kW, and simply multiplying this number with the hours of usage will give kWh. Unarguably, this is much easier than calculating everything in Joules.
Summary: It is much more convenient for the general public to find out their electricity usage in kWh than J. This also gives much more sense to these usage numbers as different appliances have different range of wattage (LED light bulb ~ 5-20W, Fan ~ 55-100W, A.C. unit ~ 900-3000 W, etc.).
A: Kilowatt-hours without time information are useless
"1 kW⋅h" does not give any information about how much time was needed in order to transform this amount of energy. It could have been either 1000W during an hour or ~114mW during a year.
Similarly, my household could also consume 12 gigawatt-hours worth of electricity. It would just need 4000 years to do so.
Watts without time information are (typically) useless

New York City uses 500 megawatts

Some duration information is also missing in this sentence. Is this peak power? Is this in winter or in summer? Is this an average over a whole year, or was it during the last 24h?
Pick the unit which allows the easiest comparison
One way or another, you probably should specify either :


*

*Energy & Duration

*Power & Duration


In theory, you could always pick the same units (e.g. W and s) but there's a very wide variation of orders of magnitude for energy and power.
People usually know how long a kilometer or a mile is, or how cold 10°C or 50°F are.
Most people will have no clue what 43TJ represent, though.
Depending on your audience, you should then pick the units and magnitudes which help compare to more tangible things, such as a horsepower, the energy content of 1l of gasoline, the average yearly consumption of a household or the power output of a nuclear power reactor.
