Contrary to public belief, INTPs do have leadership abilities. However, these skills tend to lie fallow for various reasons that we shall explore shortly.
When INTPs do lead, their strategic planning abilities, knowledge and unconventionality provide advantages to the team that are characteristically Rational. The INTP sees the long term goal for the group and devises a strategy for reaching the goal using the most efficient path they can find.
Since INTPs dislike control and rules, they tend to be casual, "hands off" leaders who set goals and tasks but leave the details of the implementation to their subordinates. (INTP leaders seldom have problems with micromanagement. They may, however, have trouble enforcing rules and reigning in unruly members of the team.) In association with this, INTPs tend to be democratic leaders, encouraging discussion and speaking with a team-oriented "we."
Keirsey (1998) has note that INTPs (indeed, all NTPs) do not tend to give orders, i.e. "Do this," "Go here," or "Do not do this." Rather, they provide suggestions, information, or advice to those under their command. "It would be a good idea to do this because..." or "We need to get this done..." and "It's not a good idea to..." For this reason, Keirsey called the NTPs the Role Informatives.
What do INTPs see (or not) in leadership? It isn't about the status. They don't get high on control. They aren't interested in the "people" aspect of it. They don't like dealing with the daily details.
What INTPs enjoy about leadership is not being controlled by anyone; getting to see their ideas carried out; and analyzing and manipulating the complex systems inherent in a large project/task under their control. Alternately, an INTP may decide to take the lead simply because they cannot stand the sight of the ship careening merrily towards the rocks.
INTPs often express the opinion that they would like to be advisors to a leader who has the extraversion, charisma and tough skin that they lack. (For example, INTP Spock was the charismatic ESTP Kirk's second in command and advisor.) Or, if the leader is not competent, then the INTP's preferred role would be similar to that of a puppetmaster controlling a figurehead. (For example, in the Three Musketeers saga, Aramis, the third Musketeer and an INTP, was planning to create a puppet king for himself. Similarly, Mycroft Holmes, Sherlock Holmes' obscure brother, was described as occasionally being the British government.)
One can also find real life examples of this relationship; for instance, Albert Speer (INTP) was one of (ENFP) Hitler's closest friends and managed the German homefront while his Fuhrer fought the Allies. Speer shunned the limelight and avoided public speaking like the plague, but his silent success in keeping the war machine running allowed Hitler--an unquestionably charismatic leader--to carry out his plans for destruction.
Generally, however, INTPs tend to view leadership as being more trouble than it's worth. In addition, Rationals have high standards and tend to be critical of others, and thus INTPs tend to worry about criticism themselves. The social demands of leadership may also weary them. However, INTPs can be capable virtual team leaders because of their above-average written communication skills and the fact that the distance offered by the internet mitigates the interpersonal factors that might otherwise cause trouble for them in real-life interactions.