My understanding was that the watt-hour meter actually measure VA-hours.
I
asked the electric company once, and that said that was the case. But I
wasn't speaking with an engineer.

FWIW, Energy Australia responded to my query as follows:

"Most residential classification customers are metered by a spinning
disc meter, or a basic electronic meter which does not have enough
'smarts' in the meter device to enable billing to be carried out at a
KVA pricing.

Currently small customers are billed on KWh pricing, and KVA
Demand pricing usually relates to large commercial and industrial
installations where poor power factor may impact upon the EA network,
and there may be an economic billing benefit in the customer pricing
to ensure that Power factor is closer to Unity."

This is really confusing. Looking solely at the second paragraph, the
implication is that industrial metering is at the VAh level, not Wh.

I don't think this person really knows what he's talking about. The fact
that his statements are redundant ("a basic electronic meter which does not
have enough 'smarts' in the meter device") and jargony strongly suggests
this.

Nevertheless, thanks for asking. I think I'll call the Seattle utility
again.