I believe countries which don’t do explicit exit passport checks are the exception rather than the norm.
Beyond the US, there’s also the UK not doing it, and Ireland as well I believe.
At least in the case of the US and the UK, authorities get the list of people who exited from the carriers in many cases (that’s relatively recent in the UK, before that they just didn’t know).
The goal of those checks may include (that varies a lot):
- to prevent some people from leaving. In “free” countries it’s usually wanted criminals, in authoritarian regimes it can be anybody who wasn’t authorised to leave.
- to check that temporary visitors did not overstay their visa. If they did, the reaction could range from “we take a note and good luck for your next visa or visit” to fines (and possibly jail until you pay)
- To check that children are not taken out of the country without the proper consent
- To stamp your passport: believe it or not, in Schengen, at this time, the only way to find if someone has overstayed the 90/180 rule is… to find all entry and exit stamps in your passport and count the days!
I believe India has special rules for some categories of people/passports going to certain countries, but I’m not familiar with the details.
Indirectly, it will also tell authorities who didn’t leave and could thus be in violation of visa terms, though other than stats I don’t think this is currently actively used (it requires quite a bit of IT and processes, and there are so many reasons one could appear to not have left the country without being in violation of their visa that it would probably result in too many false positives).
Officers performing passport checks are usually not the same as those performing customs checks (though they can refer you to customs or alert them if they have any suspicions).
Systematic exit customs enforcement is extremely rare (even on entry, in many countries most people are just waived through). It has happened to me a few times to have customs officers at the gate asking questions. Mind you, it was a flight to Las Vegas and they were inquiring about large amounts of cash.
Some countries will have higher levels of enforcement, either about historical artefacts, or protected/endangered species, or even drugs, but usually they just count on the destination country to catch smugglers.
The people doing security scans are yet another set of people, in many places they’re not even government employees. It may happen that customs either “piggyback” on those checks or have their own checks, but again, usually not as frequent.