The number of people killed by either gators or grizzlies each year combined can be counted on one hand, but people take freakish anecdotes and inflate them to sound like they're the greatest danger facing people today.
Alaska would be a less interesting place without its grizzlies and Florida would be a less interesting place without its gators. Those who want to eliminate either because of statistically negligible risk (compared to say, the real safety risk of having inner city neighborhoods nearby) are typically "safety moms" types who want to create a world that's more like a padded cell for their kids.
I grew up in FL and we all knew to stay away from gators and snakes. Not one person I ever knew got attacked by a gator or bitten by a poisonous snake.