Kilowatts per hour isn’t nonsense.
Well, it isn’t necessarily nonsense, but the occasions when it can be used meaningfully are much rarer than the occasions when it is used nonsensically. To be meaningful, the user has to be talking about a rate of change of power (power being rate of energy (used or generated) or work, and thus already containing the element of “per unit of time"--the watt, a unit of power, is a joule per second).
So you might reasonably say something like “The electricity generating capacity of Lichtenstein is growing at so many kilowatts per hour,” or “The output of the failing reactor is declining at so many kilowatts per hour.”
However, one more often hears it in the form of “The reactor can produce so many kilowatts per hour” (or “… per day"), which is nonsense.
It is certainly not just another way to say “kilowatt-hour”, as OPT and RH have already pointed out, and confusing them really is “all that bad.” It’s like treating “feet per second per second” and “feet” as synonymous.