I had a client pause in a coaching session last week, she leaned forward and then said, "Do you mind if I ask you a question?" Of course it was fine to do so. Then she asked, "Can introverts be effective leaders?" Now that's an interesting question.
I know why she asked it in that she perceived that introverts tend to be more inward looking and deep thinking and as a result are not as expressive or outgoing as their extravert counterparts.
Nevertheless, it is clear that introverts can make very effective leaders. Firstly, many introverts have very effective communication skills. Being introverted does not mean in any way that an individual can't communicate well. They can meet and greet as well as any extravert might do. However, it is true though that social interaction can deplete the introvert's energies faster than for the extravert and they do need to find some respite at times, but nonetheless, they can be effective communicators.
In cases though where the introvert might be more withdrawn and somewhat distant and not have learnt to communicate effectively, then I've seen that person appoint a more social, friendly individual as the second in charge or the deputy in the organisation. That arrangement tends to work well in that the introvert as the deep thinker tends to undertake much of the planning and strategy while the 2 O-I-C communicates the message down the line and to the rest of the company or organisation.
Yes, both introverts and extraverts make very effective leaders. It's all in the art of communication.