I agree, I worded it poorly.
The point I was trying to make is that there is no specific time which is relevant to the usage of a number of watts. The definition of a watt uses 1s as the time for which an amount of work is done, but there is no time whatsoever implied when an electrical load is described as 1W.
Yes, 1W = 1J/s, but since Joules don't get used in electricity tariffs, or appear on bills, you could just as usefully say that 1W = 1kgm²/s³ for all the good it would do.
A 15kW heater is converting energy from one form to another at a rate of 15kJ/s. Or 54MJ/h. Or 15J/ms. Or about 51,182Btu/h
So while you can equate a number of watts to a rate of work, i.e. to some amount of work per unit of time, there is no time component of a number of watts.
A 15kW heater is using 15kJ/s. It is not using 15kW/s, or 15kW per hour, or 15kW per day, it is using 15kW.
Your kettle is consuming 2.2kW. Not 2.2kW/s.
If it really was doing something described as 2.2kW/s then it would not be able to do it for very long, as the fuse in the plug would blow after a few seconds - a W/s figure is an acceleration.