The problem with this happening at all in the US:
The main issue I see here is that cheap corn and cheap soy are driving the flood of ultra processed and calorie dense, designed-to-be-delectable food into the US market.
Cheap corn and cheap soy are cheap because they're subsidized by the gov't.
For the gov't to start taxing those products, it would be counterintuitive. For the gov't to stop subsidizing those products, farmers would revolt. Or at least get poorer than they already are (except for the factory farms). The factory farms exist because people realized they could grow mass products including corn and soybeans and snatched up all the land they could to mass produce and mass process monocultures. Like corn and soy.
If you're a small farmer in the farming cycle you're caught in the farming cycle which is pushed in no small part by gov't subsidy. You're broke, forced to buy seed that's expensive and can't be saved, forced to grow certain crops because that's what guarantees at least some money, and once the money finally comes in from sales and the gov't you have to buy a new round of seed again.
It's simply not logical for the gov't, with its left hand, to offer subsidies for crops which are used to fuel terrible food, then turn and with the right hand tax the products of those crops and drive down demand/attempt to limit consumers. Gov't needs us to eat as much corn and soy as possible. Every year US produces huge huge surpluses which is how we figured out how to make so much terrible stuff like HFCS in the first place.
The gov't is effectively already subsidizing terrible food and nutrition available en masse to make gen pop obese. They can't choose to make the population healthier with health taxes when they've already chosen to make the population engorged.