Sysadmins have a love/hate relationship with logs. We spend hours and hours every day diving through them looking for clues about what happened that shouldn’t have, what didn’t happen that should have, what systems and people are actually doing, and gauging capacity for the future.
It’s one thing to look at one log for one particular issue; but some complex issues lead a merry chase through many logs or many servers which can get very complicated very fast. To ease that burden, all but the simplest of setups should employ some form of log centralization. Centralized logs are easier to access en masse and they’re easier to bring analytical tools to bear to pry out their secrets.