Let's take this dimension : Control

EP : Expressed LOW, Wanted LOW
EJ : Expressed HIGH, Wanted HIGH
IP : Expressed LOW, Wanted HIGH
IJ : Expressed HIGH, Wanted LOW

This gives 4 main styles of leadership :

EP : democratic and creative ; lets initiative go and is initiating himself. Initiative-based
EJ : wants everyone, including himself, to be assertive, productive, and efficient. Efficiency-based
IP : holistic, globalistic, and flexible ; wants everyone to have the best place and role he could have at the moment. Harmony-based
IJ : autocratic, wants an organisation which is stable and durable, no redundant changes or risk taking. Stability-based

On a socionic website I read "it's desirable to give leadership only to extrotims" ; this is not totally wrong, because most introtims have either a weak and laxist (IP) or passive-aggressive (IJ) leadership style.

My school was led by introtims and even if in global meetings (with most staff AND students), when we talked on the problems the school had to deal with, staff tended to say : "We acknowledge that, will reflect on that, and do anything possible for that". But effectively, they did NOTHING. 70% of that staff were introtims indeed.

I didn't say all introtims should be excluded from such roles ; for example, my father is an ESI, and he ran his own business since 1987 ; as far as I know, very few complaints have been made, on staff, suppliers, and clients. He has good relations with them.