Kagura:
I'm sure it did in the early years, but remember that this has now been going on for the better part of a century, and the fiefs are essentially kept in such poverty and divided that any rebellion would be very simple to put down. The reasoning behind the Games isn't really explained all that well until the second book though, so if you only read the first, your frustration with the motive and implementation makes sense.
I guess I'll have to finish the trilogy to have an opinion on the entire trilogy, however, it seems that a rebellion of some magnitude does occur, and I think that the games play a roll in the creation of that rebellion.
Kagura:
They allow the acts of compassion because even the target audience (the people of the Capitol who don't have to sacrifice their children to the Games) need compassion/romance to make interesting television. Also, that dynamic has the added draw of being a unique situation for a yearly murderfest show.
The games are first and foremost propaganda. The source of the entertainment should support the propaganda not the other way around.
Kagura:
As for trying to kill them once they figure out that Peeta and Katniss aren't willing to kill at all costs, they do try that, but again, if the game makers get directly involved then that wouldn't make good television, especially since it isn't clear to the game makers until the very end that the pair have TRUE compassion for each other (think about it, the readers only know how Katniss is feeling because she's the narrator, but even the one person who is supposed to know the competitors best - their sponsor - treats the romance as a tool, not real emotion). The attempts to kill the two are therefore limited in scope, but they go from drought (to force them into the waiting weapons of the other remaining players) to an outright attempt at massacre (the mutant dogs... which were actually almost successful in killing the two).
Katniss's final play, the poison berries, was completely outside of the sort of thing that the game makers would have thought of, partially because that's not part of THEIR lives, and partially because NOBODY is supposed to have that kind of knowledge. Remember, Katniss and Gale going outside the fence in 12 to hunt was illegal.
The gamemakers easily could have rigged the game. The simplistt way would have been to told the other players off camera where Katniss was hiding. The gamemakers only have to maintain the appearance of not interfering. (Although everyone seems to already believe the games are rigged.)
Also, Katniss using a ton of effort, time, and her sponsor money to heal Peeta should have told the gamemakers something strange was going on.
Kagura:
Again, I thought this decision made sense for the world the book was depicting. Killing the two remaining contestants would have set an unacceptable precedent for the Games and most likely WOULD have caused riots and rebellion. Remember again, that, for the Capitol audience, Katniss and Peeta are sympathetic characters. To kill both of them would have unsettled the Capitol because, if one of the rules of establishment was broken (by the Capitol allowing all of the Games contenders to die), then the stage would be set for ALL of the rules of the Games to be broken, including the one that said Capitol children were safe from the Reaping.
It would also have caused problems in the districts because, as you pointed out, Peeta and Katniss had become heroes of a sort for the districts. To kill them would have almost certainly united the districts, which was exactly the situation that the Capitol was attempting to avoid by allowing them both to live.
If they had eaten the poison berries then the gamemakers could say that they weren't allowed to interfere at least on such short notice and both would have died with little blame on the government. Anyway two people surviving is breaking the rules as much as one surviving but contradicts the message of the games.
Kagura:
The "glorification" of the victors was more of a tradition, and again, to flaunt that would have been to allow an opening for unrest, so once the decision to allow them both to live was made, there was no other choice. However if you'd read the next book you'd have learned that, not only did President Snow attempt to use them as a propaganda tool, but he also threatened Katniss in person back in her district (by threatening the safety of her mother and sister) to keep her in line, although he never trusted her to do as he asked, and so kept her under close watch. Also, he managed (theoretically) to manipulate the next Games so that the competitors were former victors, sending Peeta and Katniss back into the arena where the game masters did their level best (although the head game master turned out to be an undercover rebel) to DESTROY the two completely...
They could have at least downplayed the victory while plotting to kill the two of them. I think they could have killed Katniss in the hospital after the games and come up with a rare medical accident that occurred. (Maybe she was allergic to a medicine in the procedure or shock put her into a coma. They could have come up with something.) They decided that breaking the most important rule in their game was a great thing, and I don't see how that helped the government at all.