No,It's not so much about wax protection etc. It's all about what the product is designed for.
For instance, washing up liquid is designed for removing food that is dried/baked onto pottery and pans. Usually, pots and pans etc are much tougher than the finish on your car and can stand much harsher detergents.
I know that washing your car with a Dawn will remove waxes and other sealants, but that is only intended as a one off deal. Many washing liquids use salt as a thickening agent and it's not something you want to wash your car with on a regular basis.
I'm not sure about what damage hair shampoo could do to your paint, but it is formulated to solve quite a different problem than removing automotive soiling from paint.
Car shampoo, on the other hand is designed to remove the type of contaminents that your vehicle will encounter out on the road from your delicate paintwork. Furthermore it is designed with lubricity to enable you to rinse the soap and dirt from the paintwork without scratching.
It's the right tool for the job. And as has been said earlier, you might as well because there's a lot of car shampoos out there that are cheaper than a lot of the household alternatives that people seem to be using.