Natural immunity isn’t a singular binary consistent thing: it varies greatly in duration and effectiveness. You have some natural immunity for some amount of time after you get COVID, but that is nowhere consistent as can a vaccine will give (and its much easier to track vaccine effectiveness, adjust as needed, then each individual’s natural immunity response). And vaccine are still beneficial to those who have natural immunity.

Authorities aren’t trying to “trick people”, they are manage an epidemic with more of a sure thing (vaccines) rather than something that is much less reliable.