In theory you could track every single person who had been exposed and force them into quarantine until you were sure they weren’t shedding virus. But in practice you’re right. Vaccine and treatment options also help a lot in contact tracing and quarantining, because you can tell the people whose lives you’re disrupting that you will do something good for them.
(I remember reading reports of the eradication of smallpox – they would find cases and quarantine them, but they wold also vaccinate the entire village/neighborhood where the victims lived, so there was an incentive to report rather than cover up.)