First, sometimes it is necessary for an organization to negotiate with other organizations. If an organization is large, then it is highly impractical to have all its members at the negotiation table. Being able to represent an organization during negotiations is a position of power, and in any big organization, there will be individuals competing for power. When there are individuals competing for power within an organization, they are strongly incentivized to use help by people who are outsiders relative to the organization. Members who want to get a higher position within an organization always end up allying with people from outside the organization, who might help them get to the higher position they want, but, such alliances are fundamentally hostile to the goals of the organization itself. The only way to avoid leaving an organization open to outside influences is to have a supreme leader. Second, without any official authority (granted democratically or otherwise), it is much harder to keep the undesirable types of people out. If one member tells a newcomer "You don't belong here. Leave." and another person says "You are being mean towards this person for no reason." then no time-efficient solution that is to everyone's satisfaction is possible. It might be possible for a very small organization to operate without a leader, but the larger the organization, the more vulnerable it is to subversion. And for solving large-scale problems, which is our topic of interest, an organization will most likely have to be large.