I used to be on the anti-American cheese hate train until I started trying to level up my burger game -- I make better-than-restaurant quality burgers now, if I may say so -- and discovered J. Kenji Lopez-Alt and others explaining what American cheese is and how to replicate its meltiness with any other cheese.
Short answer: American cheese is cheese, it's just got a sprinkling of a naturally occuring powder that makes it melt more easily. You can order the powder for yourself off Amazon and make Cheddar or any other cheese melt the same way or even extract it from non-flavored Alka-Seltzer to add to your cheeses.
Every burger chef I read or watched on YouTube swore by American cheese as the cheese to put on burgers because of its even melting properties and many of them came prepared with long answers about American cheese, since they've heard these complaints before.
(For the record, I use Colby pepper jack on my burgers, but have American cheese I use when asked.)