Hunger Games Reaping Plot Hole

Panem features two tributes, a girl and a boy from each of the twelve districts, selected on reaping day. The reaping uses a lottery system, drawing random names from 12 to 18-year-olds. This is described in 'The Hunger Games Reaping Plot Hole'.The Hunger Gamesbook:

You qualify for the reaping when you turn twelve. That year, your name enters once. At thirteen, twice. This continues until you reach eighteen, the final year of eligibility, when your name enters seven times. Every citizen in all twelve districts of Panem follows this rule.

The novel shows age is not the only factor in entry counts. Katniss states this:

If you are poor and starving like us, you can add your name more times for tesserae. Each tessera buys a year's worth of grain and oil for one person. You can do this for every family member. At twelve, I had my name entered four times. Once because I had to, and three times for tesserae for grain and oil for myself, Prim, and my mother. I needed to do this every year. Now, at sixteen, my name will be in the reaping twenty times. Gale, who is eighteen and has fed a family of five alone for seven years, will have his name in forty-two times.

Since people can add more entries for reaping day to get more food, why won't everyone from a poor district like 12 add their names as many times as possible? Redditoru/timisplumppoints out:

…Imagine everyone doubled or tripled their name count (or multiplied by 100). The chance of being chosen stays the same for everyone. Everyone would get 100 times the food. I never saw sense in that.

The book shows entries might count by family members. This makes it unclear if one person could enter 100 times. However, a fix could force the Capitol to give every Panem citizen a year of food. Families with multiple candidates, like Katniss and Prim, could enter three extra times each for six tesserae.

Some people defended this idea by saying this reaping day trick needs too much trust among citizens. Those less desperate might not agree, or they might only fake adding entries to lower their own odds. Redditoru/Mirshacompared it to the Prisoner's Dilemma, saying:

If everyone claimed they would enter their name 100 times, anyone who lied would gain a big advantage before selection.

Another Redditoru/ArgieGrit01Designated volunteers could improve their district's lives. Katniss volunteers for her sister Prim. Why not let everyone enter their names many times for food while volunteers step in at the last minute?

If you can volunteer, why don't people cheat to get food? District 12 chooses a guy and a girl to compete at the start of the year. Then, they volunteer at the sorting. This lets everyone ask for food without the risk. Volunteers can train and eat well all year.

This mirrors how wealthier districts' careers work. Two people volunteer to risk their lives without access to Districts 1 and 2 training. This seems like a clear way for poorer District 12 to improve. Gale and Katniss show people are willing to risk lives to feed the community.

Logistically, the reaping fails sense. WhileHunger GamesMovie viewers watch Effie Trinket pull names for District 12 from a fish bowl for effect, Quora userPaul RobinsonPaul Robinson points out the math doesn't add up:

Twenty thousand people fill each district. Ten to twenty percent of those people are reaping age; this estimate is likely too high. That yields two thousand to four thousand people. On average, three and a half ballots per person exist—one for every twelve-year-old, seven for eighteen-year-olds. This means seven thousand to fourteen thousand ballots total. A cement mixer truck would contain this volume, or even turn it. Yet, they reach into a glass bowl, the size of a goldfish bowl, to pick one. My guess is they collect all the ballots, mix them in the truck, and toss some in a bowl for the public reaping.

Assume this is Capitol trickery and lies, not a major plot hole.