Overstaying a tourist visa in Chile, any other penalties despite a small fine?

Besides Tom's great answer, there are two more reasons.

First is that overstay laws can change, and might introduce much harsher penalties. For example, a fine might increase 100x, or jail time may be introduced. Those changes might be implemented very quickly in certain political situations (i.e. "terrorism"), and you might not be able to leave quickly enough to escape them. Or the procedure of paying fine may change, suddenly making it very inconvenient (for example forcing you to go to your port of entry to pay the fine). Latter is especially true when collection of overstay fines is regulated by some ministry, as those regulations can change overnight and you might not even know about those changes until you appear at the airport.

Another reason is that once you overstay, you're usually breaking the law of the country. This means if for any reasons law enforcement stops you, and checks your paperwork (or you're a victim of a crime and go to the police), they may detain you, and eventually deport you. Whether this would really happen depends on the country and the area, but those things are volatile. Thus even if the country law enforcement historically was lax toward overstayers, an act of terrorism, unrest in neighbor country or regime change may change this overnight.