Rigor in definitions allows us to express a lot of complex things in a compact form. this allows us to treat “Cars” as something different than “Motorcycles” while both a motorized vehicles.
Meh. There’s plenty of room in the gray zone between “car” and “motorcycle” where things like this or this can exist. The botanical world has worked very hard to create rigorous definitions of fruits and vegetables only to be completely ignored by cooks. The culinary world in general has done just fine for centuries without rigorously specifying whether taco’s are sandwiches and cereal is a soup.
As long as it is generally understood what people mean by a word when they use it everything will be mostly fine. REST is an understood term, whether the inventor of the term meant something else by it is immaterial.
The system you are describing is what most countries use. This is basically just an extension of that intended for people who make so little they need extra assistance.
Actually, the US Earned Income Tax Credit is basically a version of negative income tax.