I learn piano and guitar (and play several other instruments). I think that aside from the effects music has on your brain and intellect itself that has already been discussed, learning an instrument teaches you other fantastic skills like perseverance, concentration, commitment, dedication, communication, teamwork and time management which also apply to other parts of your life, especially study. These skills flow into an overall attitude to life and learning.
Playing music with other people in band situations contributes further to these attributes that one-on-one music lessons cannot.
Music for me has played a very important role in 'socialisation' as you describe it. It forms an integral part of my identity and I could not imagine life without it. In my early teens, it was something I could identify with in other people and enabled me to form and nurture new and existing relationships. This has continued to be the case ever since. Music is a universal language that can connect people in ways that no other means can and enables people to express themselves non-verbally. If you analyse the role of music in society throughout history, it was always been a communal appreciation activity - from classical recitals, to rock and roll dances in the 1950s, to rock concerts. Music is a social activity.
About the "coming out of people's shells" idea, I am quite the epitome of this! In primary school, I was always the quiet, reserved one. By the time I hit high school, I decided I wanted to be a more outgoing person and music and performing became a way to do this, and has shaped the person I am today. Long story short (cos I've already crapped on heaps) I am now a rock chick and quite the socialite!!
If you haven't already figured it out....I'm probably gonna be a music teacher!! lol!