O contraire, it actually does exist. Just barely in america (ironically) today. It's supposed to be simply cheddar (usually) mixed with sodium citrate (not a big deal) as an emulsifier, and butter and milk, heated, melted, and made into squares. Makes it cheaper, more versatile, more neutral, softer, and more meltable than standard cheddar. You can make it at home.
But the shit in the store isn't American cheese anymore. It's slop. The kraft one is actually far from the worst that it can get. https://www.nutritionix.com/i/sunny-acres/american-slices-cheese/54e8cfbc852409091fc38b5c have look at this.