Air conditioners, fridges and the like have a large motor driven compressor, usually with a large start-up capacitor. These both take a very hefty current for a very short period of time at start, which is usually not a problem for old fashioned fuses. Modern electronics however may get fried. Whilst the running current of, a fridge say, is only 4 amps for a 1 kW power (240 volts nominal) the startup current usually requires a full 13 amp cable and fuse.
I have a softub (hot tub) which draws 1 kW when running, but again has a large starting capacitor to get the motor going. That and a motor starting against a load means the starting draw current is again 3 to 4 times the running draw. I use a shelly 1PM in the supply, not to switch this but rather just to measure the power. This works fine. The Shelly has protection, and has been known to switch off when it falsely detected over voltage, and again more recently when the starter capacitor packed up and the starting current exceeded the safety margin. The Shelly turned off before my consumer unit MCB did, which is quite reassuring. Otherwise my Shelly does a good job of power monitoring.
In terms of working off ‘lifetime energy’, you will have a figure that represents the total used energy in kWh or similar. Naturally it is possible to infer back to power, since power is just rate of energy use, and the derivative (fx / DX) integration can do this for you. We normally use the Reimann Sum (integration) to go from power to energy, and the Derivative goes in reverse from energy to power.
Although the Derivative would seem to be a very useful sensor, I have struggled to get much sense from it. Like most things, it works best with a consistent and frequently updated input sensor, and will return the rate of change quite nicely. For things that get switched off most of the time, the results are not so helpful. Getting the sampling rate set can be tricky.
I have, for amusement really, a ‘rate of change of SOC’ on my solar battery. This tells me the rate of charge or discharge as % per hour. I have also experimented with taking the tub power (kW) to energy (Reimann, kWh) and then going back to power (DX) in reverse to see if they are indeed inverse functions of each other. OK on a good day, and better with the time-weighted average of the derivatives option I think. Perhaps worth experimenting with?
You can find derivative as a Helper > fx Derivative Sensor.