For the same reason you don't need to have every single steak and every single carrot analysed to a molecular level. After all, each individual steak or carrot will be a little different from every other. People who know what they're doing has found that mixtures of certain substances within certain parameters are just inherently safe and there's no point in a lot of histrionics around this.

> Who decides what the library of safe ingredients are?

The FDA, as well as their counterparts in practically every single country in the world. This is not controversial.