Yes, but requiring that soldiers do so makes the process of conquest less optimized, since it’s easier for obvious reasons to get soldiers without this requirement than with it.
You seem to be focusing solely on cost; the difference between benefit and cost is what matters, and the benefits of a fighting force with shared values (particularly shared religious ones) are many and obvious.
The Mongols had the advantage of recruiting from a pool of steppe nomads with similar values.
The Roman Republic conquered the Mediterranean basin with an army consisting of Italians that were required to adopt Roman values before joining. Later the Roman legion adopted the looser system you described. Subsequently Roman legions would spend nearly as much effort fighting other Roman legions in civil wars as fighting Rome’s enemies.
You seem to be focusing solely on cost; the difference between benefit and cost is what matters, and the benefits of a fighting force with shared values (particularly shared religious ones) are many and obvious.
By that reasoning, it’s the Romans and the Mongols who are un-optimized for conquest.
The Mongols had the advantage of recruiting from a pool of steppe nomads with similar values.
The Roman Republic conquered the Mediterranean basin with an army consisting of Italians that were required to adopt Roman values before joining. Later the Roman legion adopted the looser system you described. Subsequently Roman legions would spend nearly as much effort fighting other Roman legions in civil wars as fighting Rome’s enemies.