> Oddly enough I don’t see “money” mentioned, at least not simply

"the entitlement principle (service as the flip-side of the coin for some set of rights or status)" and

the employment principle (separate from the vocational principle). We may sum it up with, “recruits show up purely as an economic transaction: service for money” – it’s a job.

Close enough.

> and that should probably be reason #1

Article goes on to explain that:

it is fairly rare for pre-modern armies to function purely ‘as a job.’

Which makes sense: humanity's history of picking fights with fellow humans goes back much further than the history of money itself. And even where they overlap, there's other reasons for recruits to enter an army.

Much of pre-modern societies were organised around master-servant, slavery, nobility, family clans & related concepts. Free market economies with individuals striving to maximize the amount of gold nuggets in their pouch, is a relatively recent concept.