I would agree with @Wildan a player can use other computer to cheat so it doesn't make sense on having a bet on a Chess game but that would be great if anyone can stop people from cheating (Which is not) for me adding a bet on Chess game could spice up or make the game more intense.
It is possible to have a this kind of game if the player could have a live webcam to them (to see if they are using other computer) and a screen share of their computer just like what they are doing in online chess tournament but that was too much right? Setting up cameras and sharing your screen to others.
I severely disagree with your first statement.
First, high-level tournaments contain super GMs who does not use any engines at all. While we may argue that they may have the possibility of using so, they are strictly monitored with their respective PCs in order to avoid such cheating. In addition, these super GMs would not want to use any engine as they are the engines themselves. In the event that they actually use one, then they would just put their whole career into jeopardy and waste all of their efforts building their ratings on the ladder.
Again, betting in chess is just as fun as betting into other sports. I just hope that people would see the potential of this sport exploding in the near future.