Introversion versus extroversion is always a topic facing any group and the balance that a group has of the two will do lots to determine the group dynamic. I believe that introverts are often encouraged to act as extroverts since I feel that America is a nation with a shorter and shorter attention span. Lots of what Cain was explaining that some of the power of introverts was their process that included reflection and time alone to think ("In the wilderness") that can lead to very powerful and profound answers to problems. I believe that the short attention span that is encouraged by our society is not conducive to this kind of process, and encourages people to be constantly sharing or just talking, evidenced also by Cain's examples of the desks facing each other or the idea that "great ideas only come from gregarious interactions." I believe that this impetus for quick action and constant sharing may come from the industrial revolution and the implications that it has had on our education system, perhaps teaching extroversion as the more efficient of the two traits for quick productivity.
I believe groups may gain the reflected and complex ideas that can only be thought up as result of introverted thinking or influence. Including an introvert in a group and having their introversion expressed can lead to these ideas or a culture that promotes them to balance the talking and discussing that extroverts may encourage. Having introverts express introversion in groups can also lead to a healthier balance of the group dynamic so that the different people in the group can contribute at different rates in order to be most productive. Without introverts, clamoring over one and other and quick decisions without an entire method of thought used.
Considering Tuckman's Model, I can see suppressing any member of the group as a misfire of storming that leads to bad norming. In a case of bad storming, it is easy to imagine people trampling those that may have softer voices, such as introverts, leadership capability and skills in general can be misallocated overlooked, leading to the group performing at less than its potential. This would not be performing at all, according to the model, and could lead to premature adjourning before the group has made its maximum impact.