If the player is allowed to bet for themselves surely will not throw their game, they will even try to perform their best because it has a double reward, the ranking, and the winning while on the contrary, if the player is allowed to bet on the opposing team or opponent, then this will only mean that the player might throw his game.
I believe that professional athletes are originally not allowed to bet either for themselves or their opponent because often times this kind of thing if allowed gives negative impact to the game performance of a player but somehow there are cases where players are allowed to bet on other games not affiliated with them.
Yes, they can bet on other sports.
I like the idea though of letting them bet for themselves, it gives more adrenaline to the player/fighter to win the game/fight at any cost thinking there is also their money on the line.
But either that is not allowed by most of the sports industry organizations. Perhaps there should be revisions that could happen in the future as the gambling industry is getting bigger with easy-to-access online gambling sites.
The idea of getting more adrenaline from betting in their own game is good but I think it is not possible because of rules, I remembered the issue regarding 322 in DOTA esports where there is a player who bet against his team where he did a match fixing and throwing and it became the reason why betting on their own game is not allowed. For me that rule is good to avoid match fixing because there are still a lot of players and team who do this for money. I don't want to change the rule for the game to not be rigged in a scenario that organization or players may cheat and do match fixing.