I think by Good American cheese they meant something more like this:

https://www.landolakes.com/products/cheese/deli-american/

It is very much a different thing than Kraft Singles, you can get however much or little of it (or various competitors) you want anyplace that has deli meats, and the per-pound cost is not that much more, last I checked.

Although some kinds of cheddar might be made in the US, I don't think Vermont Cheddar is what anyone usually has in mind when they say "Deli American Cheese."

I've had no problem getting a good melt on burgers with "good" American, FWIW.