Sounds like an opportunity for IDE makers. Add plugins to track CSS/HTML/templating, "where used" tools, and refactoring to push frequently repeated styles up into a main CSS file, or rarely used styles down into the few elements using it.
Hopefully, there are few enough classes and styles injected from a long js code chain that you can manually check the things the IDE misses. JetBrains IDEs are surprisingly good at finding things connected via common libraries in code, so I'm hopeful that IDE makers could recognize common patterns in libraries such as React and Angular (e.g. - ng-class)