Honestly I reckon they went for the wrong unit with Watts. Most things measure absolute values (e.g. miles) and then the speed is the derivative unit (miles/hour). Whereas Watts they went the other way. I reckon that's why everyone's confused and people expect to see "I use this much [stuff] in total", "this appliance uses this much [stuff per unit time] while it's on", because that's the way every other unit works.
At least for mains electricity, there is a good argument for using the derived W and the doubly-derived Wh (J / s derives W, W * s, derives Wh). It makes sense because electricity is not (for practical purposes, historically) stored by consumers, only consumed at the time of use.
For virtually all applications, the instant power is of overriding utility: power is how bright your light bulb is, how fast your hairdryer dries, how large a wire is required when building your house. (Since Voltage is constant, this could even be given as Amps!). In addition, most home appliances don't have a meterable output aside from operation time: if your run your lightbulb for an hour, you get an hour of light but that's not really something you can measure. If you run your bicycle for an hour, you've gone somewhere which is a distance you can measure!
Accumulative consumption of electricity is not really important for anything save for billing, so if you all you know is Watts and hours, Wh is a useful unit.
For transmission and distribution networks, even the Watt and Wh are relegated to secondary position, the VA (volt-amp) and VAh are more useful (since Vrms x Arms != Wrms, due to power factor/phase shift). For one bit of infrastructure, the Amps are the most important operational consideration (as V is approximately constant) and reporting as VA is useful to compare with other equipment running at a different voltage.
The SI system has the Joule for that. The real "problem" is that 1 Joule of energy is just too small to be practical in most situations, so we often resort to larger units such as a kWh (equal to 3.6 MJ).
Watts are the right mental model. Your stuff use some amount of power while running. Be it 50W for old lightbulb, or 1kW for space heater. You run this stuff for some amount during the day. Add all these up over a day for a city and you get to some total of power. Multiply it by hours and get to energy spend.
And then you can even multiply the watt hours to get costs.
Disagree. kWh is a unit most households would be familiar with. I bet the average budget-conscious jo knows their price per kWh and how many kWh a washing machine run would use up. So for a lay audience it is a good term.