*edit: sorry, misread that. My answer is not valid to your question.
original answer: because if you dont come up with these ints randomly they are sequential which can cause many unwanted situations where people can guess valid IDs and deduce things from that data. See https://en.wikipedia.org/wiki/German_tank_problem
Hence the presumed implication behind the public_id field in GP's comment: anywhere identifiers are exposed, you use the public_id field, thereby preventing ID guessing while still retaining the benefits of ordered IDs where internal lookups are concerned.
Edit: just saw your edit, sounds like we're on the same page!
Decades of security vulnerabilities and compromises because of sequential/guessable PKs is (only!) part of the reason we're here. Miss an authorization check anywhere in the application and you're spoon-feeding entire tables to anyone with the inclination to ask for it.
original answer: because if you dont come up with these ints randomly they are sequential which can cause many unwanted situations where people can guess valid IDs and deduce things from that data. See https://en.wikipedia.org/wiki/German_tank_problem