Why not just arrange an "accident" for Jonathan..

They wanted him out of the game but in a way which they could no doubt put a spin on as an heroic accidental end for a legend of the game, which poisoning would unlikely serve the purpose. It's possible from the way he decides to travel with the team for the final game he might have been anticipating a helicopter crash to stop him.

When you talk to God its called prayer...when God talks to you it's called schizophrenia...

The issue at hand was to rob Jonathan of his power by making him irrelevant. Killing him was a last resort because of the fear of martyrdom. They only resort to that in the context of the game so people don't get suspicious or just see it as yet another death in a bloodsport that often causes deaths.

The point of the game was to make everyone understand that the individual was not important. With the usual player only surviving for a few years prior to injury or death, this point was repeatedly hammered home. Jonathon as a long surviving and still on top player was a threat to that idea. The executives agreed he needed to die during a televised game.

They wanted the game to defeat Jonathan -- it was the social purpose of the game, to demonstrate the futility of the individual and Jonathan's success was raising an individual above the game, (re-)introducing the idea that the individual could triumph over the organization.

There was a scene with the directorate in teleconference where they hashed this out.

To do so would turn him into an icon (ala Bruce Lee) with a legion of fans doing as he did.

The elites did not want to create a martyr.