As an American, I will observe that it has the property of melting perfectly on a properly-cooked burger. Does great in a grilled cheese sandwich as well. Since we eat a lot of burgers and grilled cheeses, we find it to be a useful cheese and eat a lot of it. And nachos, which are often made with american cheese since, as you say, it melts great into a sauce.
Most Americans don't use american cheese on everything that has cheese in it, but it has its specific role.
If you are making burgers, i highly recommend Raclette cheese. It doesn't melt quite as evenly as analogue cheese with sodium. But AOP Raclette cheese is natural and designed to melt - and it tastes so much better than any analogue.
You can make real cheeses melt better by using powdered sodium citrate. The ratio depends somewhat on how hard the cheese is but it's somewhere around 2-3% sodium citrate to cheese.
Every time one of my friends has flown across the pond I've asked them to bring back spray cheese, they've never been able to find it! I want to experience this monstrosity, though to be fair I am an absolute savage.