Take a wilderness first aid class and you will quickly understand that everything in your pack is part of your first aid kit, and the best thing in the kit sits firmly between your ears. Prevention is the lion's share of the work. Understanding what you can treat and continue (not a lot) and what should result in engagement of evacuation procedures (a lot of things) is the crux of the thing....

Basic first aid for your average citizen does not begin to touch things like hypothermia and hyperthermia. All hikers should have a basic understanding of those and do whatever they need to to avoid them.