How does the economy in that world even function? Tiny populations, a complete lack of infrastructure, no visible manufacturing sector, and a government that is basically comprised of institutionalized muggings makes the Pokemon world seem less like a modern society and more like a failed state. How can their government fund free pokecentres but at the same time, can't contain the activities of villainous teams)

Hell, each town of repute is essentially ruled by a warlord, and the routes between municipalities are so overgrown with grass and trees-- or rife with impassable terrain --that inter-city commerce would be all but impossible. That's not to mention the trainers who, by virtue of not being able to avoid battles, act as de facto bandits.