A guy at a deli counter slicing cold cuts and assembling them into a sandwich is “processed food”. Using the term as a health concern marker is meaningless.
Even Kraft Singles, the posterchild of “processed food”, famously disallowed to legally call itself “cheese” on its packaging, what is it made of? What hellish process hath humanity wrought? Cheddar cheese, sodium citrate (a mundane variety of salt), and water. That’s it.
It’s not forbidden from being called “cheese” because it’s a bastard concoction of mad scientist chemicals that approximate cheese to ruse consumers. It’s simply cheese, literally watered down to the point that you can’t call it cheese anymore.
All that the sodium citrate is doing in this situation is acting as a binder that helps the cheese solids hold on to the water. This action is what gives many dishes, sauces, and the like their smooth, creamy texture. But use the word for that – “emulsifier” – and suddenly people think you’re trying to poison them, because that’s a scary chemical word.
Why does this product exist? Because it offers a unique melty texture that people appreciate in certain contexts. It’s a niche product with a niche function. Treat it like one.