Rate is an instantaneous value. Just as in my analogy with speed and distance.
So you have been wanting to confirm instantaneous power is an instantaneous value? OK, but no one is disagreeing with that.
However, instantaneous power was not what Sahib was talking about before. Instantaneous power is not the power we are talking about with utility bills.
You want to focus on instantaneous power. Do you have a pratical use for calculating the power at a particular instant in time? If so, state it and we can discuss the merits. Otherwise, get happy with the fact that we are discussing the active power when discussing utility billing.
Also get happy with the fact that the power the OP was talking about was true power (or average power, active power, real power, wattage, rate of consumed energy, etc) NOT instantaneous power. Power factor is real power divided by apparent power. Instantaneous power is not what we are talking about. AC power oscillates.
Nothing wrong with discussing instantaneous power and its relationship to the rest of the topics, but continuously stating that power is an instantaneous value when we are obviously talking about something other than non-instantaneous power is not productive.
Now you want to introduce that all rates are instantaneous? In what world? How about interest rates? You think interest rates mean continuous compounding?