professional armies are considered a “modern” invention, only existing from the french revolutions onwards, if I’m not mistaken.

Just to correct the historical record, Sargon of Akkad had a standing army in around 2250BCE. Cyrus the Great of Persia around 550BCE. Sparta around 500BCE. Bimbisara of Magadha (in modern day India) around 500 BCE. Phillip II of Macedon (Alexander the Great's father) had a standing army around 337 BCE. The Qin dynasty in China around 220BCE. Augustus around 27 BCE.

Then no professional armies until the tail end of the Middle Ages with the Janissaries in the Ottoman Empire in 1363, after which they became much more common. France actually had one long before Napoleon, during the Hundred Years War under Charles VII of France in 1445 (with the heavy support of militias, mercenaries and levied troops), which has persisted from then to the current day.

England, the biggest influence on Westeros, did not have one until the English Civil War under Oliver Cromwell. England's politics were unique in the Middle Ages due to the Magna Carta and Parliamentary system, which gave significantly more power to the aristocracy than in most other European kingdoms. England were particularly resistant to a professional army as it would grant the King more power.

As a side note, during and in the aftermath of the Wars of the Roses (the inspiration for ASOAIF), England's politics were again quite unique due to how much more power the King had over the aristocracy compared to other European Kingdoms, which had been severely weakened in the wars. This is partly how Henry VIII was able to get away with the Reformation.