They really are not the best speakers, but they have other nice qualities that are perhaps even more important than a silver tongue. They are motivated by productivity, not ambitions; they measure success with a different measuring stick in the sense that introverts care less about recognisability and professional growth and more about the productivity of their team and the quality of the work that it does.
There interpersonal relationships are more sensible; introverts do not care about how many acquaintances they have, enjoying eye-to-eye conversations and knowing more about their employees than extroverted managers do.
Their attention cannot be diverted as quickly, because it is easier for introverts to concentrate to the point where they can focus on things even in an open plan office; their motivation is also easier to uphold, because quality is more important to them than quantity.