Why do we measure electricity in KWH and not in ampere-hours?

Electricity is measured in kilowatt-hours (kWh) because it’s so easy to convert across all spectrums of electricity usage. One kilowatt-hour is equal to one kilowatt of power used for one hour.

On the other hand, batteries are measured in ampere-hours (Ah) because it’s an indicator of the energy storage capacity of the battery.

Ampere-hours would refer to how many amps minimum you can draw from a battery at full charge for an hour before it was no longer capable of providing that level of flow.