I think that all this back and forth debate/arguing may have dredged up the real reason for the FF to not be executed.
Several people have mentioned little pieces of the puzzle: the UFP generally doesn't use capital punishment. The Klingons and Romulans clearly have no problem with capital punishment, and would want her executed for her crimes. The FF herself would no doubt prefer not to be executed, and would want to simply be imprisoned by the Federation. But she is the prisoner of all three powers as a POW, technically, and only agreed to become a prisoner in exchange for Odo going through the wormhole to cure the Link. Meanwhile, the Jem'Hadar certainly wouldn't react well to her death, or to the disease in the Link being allowed to continue... though they need white to survive, which is provided by the Vorta. Speaking of the Vorta, they are probably all going back through the wormhole after the papers are all signed and everything... back to the GQ, where the rest of the Dominion resides. The rest of the Dominion, and the rest of their Jem'Hadar + battle fleet. They know that together, the Feds, Klingons, AND Romulans could keep them at bay... at the same time, all those AQ powers know, in turn, that though they could prevent the GQ Dominion forces from completely overwhelming the entire AQ if necessary, it would be EXTREMELY bloody and extremely costly. Then there's the Prophets, who are basically a completely unpredictable wildcard.
Put ALL this together, and what do you have? A balance of power. A stalemate.
No one will execute the FF, because it would upset the balance. This rather precise arrangement is a compromise that is in the best interests of EVERY power involved in this thing to maintain.