I've had this thought before, when seeing labels that talk about kWh/day. The answer is very simple: you pay per kWh. When people want to know power efficiency, what they really want to know is "how much will this cost me to run?". That answer is most easily expressed in kWh per unit time.
Also giving an averaged power drain would be misleading. If the device uses 2.4kW but only for half an hour per day, that's not a 50W device as far as cabling, fuses and other electrical considerations.
In the US, at least, there are some utilities that charge based on maximum kW (demand) and total kWh used (energy). ComEd in Chicago is a utility with a demand rate plan option.
That tends to be commercial rates since businesses can have larger spikes in consumption, so the "pipe" needs to be larger. Industrial rates are similar.
There are some like ComEd that you call out that can apply the model to residential rates, though my (now dated) experience is that they are rarer.
Knowing the average of 108 W wouldn't help with knowing your peak demand, as fridges vary significantly from off to startup to running, so knowing the average isn't useful in that situation either.
It would be completely wrong for peak demand. I had to learn this the hard way. While the small fridge I bought only uses 80 W while running the compressor uses 800W+ for a second on startup which was too much for my off the grid inverter.
That strain does not seem to be reflected in the usage, which has been in a shallow decline since the 90s. Maybe they could consider using smart demand management, which is becoming popular with a lot of utilities to move usage away from peaks and into the quieter times.
I think these tariffs are meant to encourage exactly that. Note also that there are many levels of bottlenecks. One could be in your neighborhood, if all your neighbours have EVs.
Perhaps it will work. I'm just a bit skeptical because it seems unlikely to be a widespread problem. The average driver in Sweden will only need perhaps 6 kWh per day, which at L2 means charging for 35-40 minutes. A bit of demand management from the utility and everyone in the neighborhood can get what they need without stressing the local grid. Or just knock down the rate to something inconsequential and let it trickle all night.
