I look at it more like a set of options to be balanced and compared, or like a pallet of colors that a painter mixes and uses. If you have a lot of deficiencies in nutrient levels and a large lawn (acres), it may be prohibitively expensive to use the "best" fertilizers (top ingredients) for a couple/few years until the levels rise to reasonable levels. That may not apply if your lawn is 3000 sq ft - the increased costs will be tolerable. In the large-lawn case, using cheaper ingredients carefully will keep costs down and avoid the possibility of the lawn owner quitting the remediation process, and then switch to higher-quality fertilizers when the "tweaking/maintenance phase" is reached. Optimal? No. Pragmatic? Probably.
Research tells me the definition of a salt is any chemical compound with a positive and negatively charged ion, which means all fertilizers are salts, right?
If by "chemical" you mean "synthetically produced chemical", then yeah that's probably pretty true. But numerous fertilizers are organic molecules of chemicals (soy bean meal, feather meal, Milorganite, Bay State, etc) and while they are technically "chemicals", they have very, very low salt indexes - Milorganite has a salt index of 2, IIRC. They use the Nitrogen Cycle and the microherd to convert the organic molecules to available nutrients. But they are slower to act and tough to use alone in an extended remediation program.
So, there is a place for lots of fertilizers, but it takes a bit of thinking about where they fit in your lawn's planning.