In terms of arbitrariness, note that your "traditional" units are only actually defined in terms of the SI system ("metric" units). Metrication is expensive and although the US is rich it declines to spend the eye-watering sums it would cost to do adequate metrication separately for its own unit system, so the pound is defined as some number of kilograms, the inch is defined as some number of metres and so on.

As a result to the extent all the systems are arbitrary, all the traditional units are automatically one step more arbitrary.