It is absolutely not the case. You generally have to pass a competency test, and, having done that, your retention is a matter for your local police force and governed by its collective bargaining agreement. Some states can "decertify" police officers, mostly for committing a felony, which is a batshit standard.

The point of licensing is to bypass the CBA; the state can revoke a license --- for reasons other than "failed an exam" --- and having done so, the local department cannot retain the officer regardless of the results of labor arbitration.

This is something Illinois is working on right now, at the behest of the Lightfoot administration, though I haven't seen much news on progress. It's a big deal.