My parents attempted that with me, not the can-roulette part, but I was a picky eater, so in order to get me to eat new foods and expand my palate, they would give me food and say, you're not having anything but that. You're sitting at the table till it's done. While they ate food that I definitely did like.
They ended up giving up on it because I would sit at the table for hours on end and even sleep at the table. And due to the fact that I don't feel hunger until im basically almost fainting, I would basically put myself on the brink of feeling faint, which concerned them.
I'm no longer extremely picky. I'm still picky, but no longer to the extreme extent that I used to be.