Same reason we give fuel efficiency in e.g. litres per km rather than square meters.

"20 MPG is about 0.1 square millimeters," according to https://what-if.xkcd.com/11/. "If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube."

It's simple dimensional analysis (https://xkcd.com/687/).

So, X litres per km is X * 10^-3 m^3 per 10^ 3 meter. Which is X * 10^-6 square meter.

Cool. So my car has a fuel efficiency of 0.000007 square meter :D I love it.

It is, but that doesn't necessarily make it easier to use. If you have a factory producing batteries totaling x Wh/yr in capacity and every car needs a battery with capacity y Wh, then you can build x/y cars per year. The calculation is mathematically the same if the production is specified as z W (where z = x / 8766), but not as immediately obvious to understand.

Can I just quickly invent a “Watt-Hour Capacity(WhC)” and rephrase this as “40GWhC/yr”? (expecting “technically but please don’t”)

No, units don't work in this way here

You're not discharging the battery through a whole year

They are in fact equal as dimensioned quantities. Whether the comparison is useful or not, that doesn't make the rates unequal.

Not quite.

Watts are an instantaneous measurement, but the factory needs a higher output most of the time to cover downtime. Much like power plants you would say it’s capacity is X watts with an expected capacity factor of Y%.

You could say the output is expected to average X watts over a year, but to then use it for anything would mean converting that to Wh.

I mean, Watts are a unit. All of the things you are saying are important considerations when discussing the factory's pattern of output, but ultimately, as you point out, it is still valid to measure the average output in Watts, which is the point that is being made, that that's the dimension that quantity has; you can still write down an equation of dimensioned quantities even if real-world complications mean that the equation is not as meaningful as one would like!

If you’re describing the W output though you could be describing the average [charge in each battery (W*h) X the number of batteries / time period] . That’s the actual W output of the factory as actual energy.

Capacity created per time period is a different unit created as a discrete entity with each battery but having no instantaneous value.

That's not what a unit is. A unit is just a standard against with other quantities sharing the same dimension can be measured. Anything with dimensions of energy/time can be measured in Watts, not just instantaneous power in the usual sense. Whether comparing two such quantities is meaningful may, as you point out, be another matter, but they can still be expressed in Watts.