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Not really, no.

When the original swiss guys were working on their version, they were explicitly seeking to extend the length the cheese would remain edible.

When Kraft came up with his version, the same goal was in place. He wanted to be able to ship his products farther.

If anything, his use of trimmings was a side-effect that made it cheaper originally, not the other way around. He used excess cheese during his attempts, which was a cheap supply. But the emulsifier itself doesn't do anything to make it cheaper. I'd even debate that the heating process that halts the breakdown of cheese made it much cheaper by itself, but rather as an offshoot by reducing wastage.

All of this is pretty well documented, and not just by the Kraft company. There's records of the Swiss guys, their process, and communications. They were explicitly working based off of fondue, and how it lasts. The shelf stability of it comes from the the heat used to process the cheese, same with fondues. That's why they worked with chemicals that would interact with the calcium that lets casein hold the milk fats together; the old school fondue was done with tartaric acid (which is a byproduct of wine making, iirc). They ended up using sodium citrate.

I mean, unless you've seen documentation I haven't? I cobbled all this together from online sources, which means translations of the swiss stuff, and mostly excerpts in that regard. The Kraft stuff is in English, and they used to have their records online, and there were copies of that used in news articles and such over the years since a lot of publications moved online. But I definitely never saw/handled the original documents, and I don't doubt that there are plenty that weren't online when I first looked into things years ago (the comment I linked was a mini version of a project I did for a class, based on stuff I picked up from family that run a dairy).

Edit: here's a link to Kraft's patent from 1916 for his pasteurization process https://patentimages.storage.googleapis.com/a8/45/8a/3471c3db9f16a3/US1186524.pdf

Isn't it a very low percent? We use 5% of the cheese's weight in sodium citrate to make the cheddar sauce for our cheesy, beefy burritos at home.

Unless you mean the milk (or whatever substitute) it's emulsified in?

(We were able to cut down on the milk and get a much stronger cheddar flavor compared to the previous cheese, milk, and corn starch version we used, but we still use 60% of the cheese's weight in milk which does of course still dilute it a bit.)

Considering the minimum for calling it American cheese is 51% cheese, and we end up around 60% cheese, I don't think the concentration is too low. You could just use cheddar on it's own, but I think for both burgers and burritos the emulsified version is worth the milk dilution. Especially with the cheese sauce being nicely heated and spiced up with chili and a few other things.

I used to think American cheese was ridiculous, too, before I watched an Adam Ragusea video about why sauces break, wherein he had a part about cheese sauces, and demonstrated the "natural" way to get the emulsifying salt from lemon juice by heating it mixed with baking soda and tasting until it's no longer tart... I think it was?

Either way we tried a few times, it was difficult, but then I just bought a small container of sodium citrate to skip that step. Immediately changed my mind about emulsifiers after trying it. It was just nice. A really silky, awesome sauce.