I encounter these same thoughts. I have found that people really do appreciate the gifts I give that I have created and whether it was made specifically for them or not. My gift giving goal is to always make it meaningful not just to give something because it is expected. That is where my over-thinking comes in. What is meaningful to me may very well be over the top of anyone else's standard.
As far as receiving gifts of art from others...I do understand what you are saying. That actually happened to me the other day. I guess I go on a case by case basis.
You got it! I agree on the case by case basis. Each situation is unique.