Do the majority of the plants we see have healing properties?

Not neccasarily: Remember that plants develop their own special properties as they evolve to assure their survival, not for our purposes. Poison ivy is something that is very common but it is not something commonly used to heal. Many plants have effects that actually slow down or stop healing. I do not recommend you go into the forest and start eating what you see. There is research on those plants that can help.