It's a simple statement the watt is an instantaneous value.
That is not a matter of opinion.
Not only is it opinion, it is unsubstantiated opinion. I have given you examples of the use of instantaneous and average watts. Many more to be found with a simple search.
I had a quick check back through the thread and found these comments:
Rate is an instantaneous measure as in miles per hour or RPM
gar made some further comments to elaborate.
Both average and instantaneous rates exist. I have a library full of books going back to the turn of the century showing that and there are even more references to be found on the internet. Mountains of it.
Perhaps you should just accept and move on.
I'm not in the habit of accepting opinion that is in conflict with mountains of contradictory evidence.
Your statement that "Rate is an instantaneous measure " is a misapplication of concept in this case and tries to apply the concept of what some might call a "true rate" to a value that simply does not fit. As I have stated, there are both average and instantaneous rates (really, just look it up).
To summarize what you will find:
When we have an instantaneous measure we try to reach the theoretical point where the time delta approaches zero (i.e., the individual points along the sinusoidal power waveform). Trying to make the concept of a point
at a specific time limit stick to a value that is the
average of those points over a time period is a misapplication.
You simply can't throw out the time dependency of the average value because there also exists a different application that uses the concept of instantaneous change to get an instantaneous value, even if the two use the same units of power.
This is further emphasized by the fact that the power in an AC system is varying. The instantaneous change is not usually the value of interest but it is the real or average value that is of interest.
In addition to the time dependence or real watts and that we have to consider times in cycle multiples, as we shorten the time interval from periods like hours, minutes, seconds and on down to one cycle (the smallest interval we normally consider) we will find that the maximum kW value increases. An obvious time dependence for that watt measurement as well.
A value obtained by averaging instantaneous values does not transform the resulting value into an instantaneous value. It is still an average value.
Another way to clarify it to recognize that a set function does not become a point function just because they have the same units for the resulting values.
An one more way to look at it is that the slope of a line tangent to a curve at a particular point, and the slope of a line between two different points are not the same thing.