

In the absence of a king, the stewards had the same power and authority as the kings and the position was hereditary. The stewards were effectively just a dynasty in the kingdom. Aragorn’s ascension to the throne didn’t really impact the way Gondor functioned.
The real republic is actually The Shire, which is consistently depicted as the best place on Middle-earth and the only place that regularly produces people capable of resisting the One Ring.
You see this with video games, too, where PC games are better optimized when they’re multiplatform releases that also are on one or more consoles near the end of their sales life, just because they had to make it run smoothly on hardware that was comparatively out of date.