That's the point of postcodes, they tend to based on population density and, unlike electoral wards, they remain pretty fixed. If you look at the postcode areas for Liverpool (or Manchester) you'll see the size is small in the city centre, larger as you get to the suburbs by the Green Belt and then they expand out into rural areas. If you go north you can see more rural areas with towns, like PR and LA.

The sizes also reflect the range of someone's interest - in the countryside you could travel 20+ miles to go shopping, in a town it may only be a few miles.

There are currently 160 countries using postal code systems, some of which follow administrative boundaries too and such boundaries could be used in places that don't have them. Essentially, all the work has been done here (often by the Victorians as they found an expanding postal system was unviable without it) and they are well-understood, so I don't see any need to reinvent the wheel or make things unnecessarily clunky.

They also have other advantages as they may contain a code that identifies a larger area (UK: counties/cities; France: departments; Australia: states) or you can group codes manually, which could give an option for a larger area sort (Home, Nearby and Region).