In agreement on your point regarding the political rationale behind the organization of the Games. But another way to examine The Hunger Games is
1 From the selection of tributes to the execution of the games, the inhabitants of the districts are put at the mercy of the regime as everything plays out as the regime dictates. On the other hand, tributes are well treated by the organizers and presented in a glamorous manner to the districts (making it seem an honor to be selected for the Games). They are punished when they flout the rules (Katniss hounded by the fiery forest when she attempts to avoid the fight), rewarded when they please the sponsors (with favorable rankings and in the case of Katniss - air drops of supplies) and put on a pedestal should they emerge victorious in the Games.
In a single maneuver, the regime is demonstrating their power and encouraging compliance to their rule.
2 Having the districts competing against one another creates a rivalry between the districts and cause them to redirect their hostilities towards the regime onto one another. (Notice that there are districts that even go as far as selecting and training tributes from young for the very purpose of participating in and winning the games.) Sort of a divide and conquer strategy I think.
To be fair, I would attribute the plot weakness to the lack of attention towards the background story in the film version. Omission of essential plot details and lack of character depth as a result of condensation is a common problem with novel to screen adaptations and that appears to be the case with The Hunger Games.
The author could be accused of plagiarizing the premise put forward by Battle Royale (alternate future ruled by a totalitarian government where youths are forced into survival games to promote civil obedience as a backdrop for social commentary).
But fortunately for her, ideas per se cannot be copyrighted.
I have not read the original material for The Hunger Games so I am unable to comment beyond that.