I think if wizards actually existed, they would seldom bother with actual curses; which seem complicated to cast and prone to backfiring. Having shown someone a little magic, they’d be very easy to trick into thinking they’ve been cursed, and the resulting paranoia, anxiety and confirmations bias would do the job. I imagine it’d be some wizard’s favorite trick. They’d gloat about it to their colleagues and they’d laugh together in their secret wizard circles.

So a wizard would need a pretty strong incentive to cast an actual curse.