All medical procedures have to be signed off on by the doctor performing them.
This is very different to "medically necessary." What you are describing is a doctor assessing that the mother is physically capable of enduring the procedure without undue risks. What we are describing is assessing wether the procedure itself is medically necessary.
I generally support the premise that people should be able to do what they like with their bodies. Most people do. The issue is the ethical status of the fetus. Many people believe it to be alive and deserving of legal protections. There isn't a clear method for delineating that, so we make a moral judgement. For most Americans, that is after the first trimester.