Catching wanted criminals and suspects as they try to leave the country. Flagging people who have overstayed their visa when they try to leave so that they can't come back. If someone tries to leave on a stolen or fake passport, it is cheaper to catch it before they exit than when they try to enter somewhere else.
I can see the "before they leave the country" part. This isn't as big of problem in the US as we only have land borders with two countries, and those borders are far away from most people. If the police are looking for you they can find you when you book/board a flight out of the US, even without exit controls. Heck, they're likely sharing that list of people of interest with Canada and Mexico so that they can be caught by the entrance controls at those land crossings.
Criminals in Panama typically hide in Parliament. They're even passing laws to ensure they can't be prosecuted for their crimes by creatively changing the statue of limitations. They make Romania look good.
