It's all about incentives. A professional athletes popularity directly translates (mostly) to them getting to play more, play longer, and make more money. On Jeopardy, if you lose you're off. The buzzer and the board don't care if anyone likes you or not. Obviously in some extreme circumstance they could kick someone off the show for spouting racial slurs or assaulting another player or something. And injury haunts pro athletes no matter how well liked. None of that changes the fact that in jeopardy there's no incentive for showmanship or PR.