Censoring is the defining nuisance of lifetime data. Look at a live customer base today and every active customer is right-censored: you know their lifetime exceeds their current tenure, and nothing more. Dropping these records or treating them as events both bias lifetime estimates badly, which is why survival analysis exists as a distinct toolkit.
Standard estimators like Kaplan-Meier handle right-censoring by construction, but they assume it is non-informative: being censored at a given tenure should say nothing about what would have happened next. Administrative censoring at a snapshot date usually satisfies this; censoring correlated with risk does not.
A related trap is left truncation: units enter observation late, so the ones you can see from early cohorts are, by construction, survivors. In customer data this appears as survivorship bias when the base includes customers acquired before reliable history begins.