Why does the rest of Latin America then consider Chile such a stable, prosperous country?

American Latino here too. Chile is more objectively prosperous than the rest of Latin America by nearly all metrics; you're definitely right there.

However, this doesn't discount the frustration among the population, I suppose. The French started rioting for 6 months last December and they also have very high standards of living. I think if people have had enough of certain government policies, and come from a protest culture (i.e. France or Chile), they will take the streets, even if things aren't necessarily 'bad' relative to other poorer neighbors.