Being uncharismatic will hurt you more than not having leadership positions. Residencies look for "leadership qualities." That could be evidenced by having leadership positions, or it can come across in the interview by your professionalism, organization, and charisma. Having a leadership position could also help with the latter insofar as it could throw you into situations that encourage the development of those kinds of qualities/skills (e.g. working on a team project that you're invested in, advocating for students to the administration, networking with peers at an AMA conference).
On another note, a lot of people will knock our AMA without a real understanding of how hard lobbying is in the current financial and political climate (especially for doctors, for whom
one in five are in society's top 1% by income), our AMA's past accomplishments, or the extent of our AMA's involvement with non-lobbying areas of medicine.
"What does it do for you?" Our AMA sponsors and appoints medical student members to the leadership of the LCME (the accrediting body of all MD programs), the NRMP (the Match), the NBME (the creators of the USMLE and shelf exams), the Council on Ethical and Judicial Affairs (the group that maintains the profession's Code of Ethics that state licensing boards and legal authorities follow as a guide for policy). Getting involved with the AMA means opportunities to get involved on things that matter to medical students. Our AMA also sponsors the ACGME (the accrediting body of all residency programs). It publishes JAMA. It maintains FRIEDA (the primary database about residency programs). It recently awarded 11 medical schools a million dollars each to develop innovative new curricula, because accelerating change in medical education is one of three core areas of the current AMA's strategic focus (the others are shaping delivery and payment models, and improving health outcomes). Our AMA actively lobbies to
protect and expand federal (Medicare) funding for residency positions.
You may remain unconvinced. Consider an analogous situation. Consider what the government does for you as a citizen, why you pay taxes, and why you vote. Your approach to organized medicine should be similar.