That is not what overcentralizing means. You're redefining it to suit what you want.Exactly, and then it falls into the category of changing the game. It's a completely different game now, one that is alien to the original. I.E., overcentralizing.
Someone could completely ignore the food and do just fine, by punishing the other player who might get greedy and go for food that was a bad idea to go for. No playstyles except the degenerate ones that people don't like (Planking and scrooging, notably) would be significantly impacted.
It would notably not become all about collecting the food, and therefore not be overcentralized.