Let
others lead small lives, but not you.. Let others argue over small
things, but not you.. Let others cry over small hurts, but not you.. Let
others leave their future in someone else's hands, but not you.
— Jim Rohn
Leadership was a central theme of LOST. Various individuals wanted to control the island, but they never said what they would do with it. For a few, there was a silence of purpose that was seen in their beady eyes.
Leadership and guardianship are two different concepts. A guardian is a person who takes it upon himself or herself to look after someone, usually a minor child or disabled adult. The guardian is a person with the authority to make decisions on behalf of their ward. The guardian fulfills the role of an interested parent in the welfare of their ward. A guardian provides the basic necessities of life to the ward: food, shelter, security, medical and educational attention. Some guardianships end when the ward becomes an adult, but some guardianships last until death.
Leadership is a broader brush stroke. A leader is a decision maker in a group of people. A leader brings to the group a collective purpose, strategy and a plan in order to for the group to succeed in its goals. Leaders can be in any walk of life: business, charity, religious or even family units. A person needs a strong personality to draw other people to their way of thinking. A leader has various tools to assume power over his followers, such as persuasion, personality, intimidation, fear, or withholding favor such as life's necessities.
LOST had many strong and clashing leaders. In chronological time, the first leader we actually saw was Eloise when she was a young woman on the island. It was during a time skip when the castaways went to the 1950s to witness the Others capture the atomic bomb from the U.S. military (which in itself is a highly improbable event). But Eloise seemed to have the final word on matters, even overruling Widmore in a challenge to what to do with the strangers. We don't know Eloise's back story, but she is one of the few characters who knows how the LOST universe works, even though she explains it in vague analogies like "time correction" to Desmond. Someone who has the knowledge, the keys to a specific universe that other people cannot comprehend, can weld great power.
Widmore made his leadership mark more in the business world off the island. As a driven personality, Widmore was relentless in getting what he wanted in the real world. As a result, he acquired a vast fortune which he then used to buy loyalty of his soldiers. His leadership in the business world was apparently all for his quest to return to the island and conquer it. Whether Eloise actually indirectly helped Widmore find the island in Season 6 is a subject of debate, but she probably did since she had the sole means of finding it.
We then have the less driven leader like Horus. Horus was the man in charge of the Dharma Initiative on the island. He still reported to someone on the mainland, but he was in charge of the island group. Or so he thought, since Dr. Chang seemed to run the construction and science operations independently of Horus' input. Horus was the man in charge when Ben arrived on the island. Ben would later see weakness in Horus' power structure, which probably led Ben to devise his purge.
Ben was a role model for dictator leadership. He ruled with the iron fist of fear. He got the Others to follow him because he showed them he could kill without emotional strings, such as killing his own father. That act of rebellion seemed to be the new caveat for leadership of the Others, as Locke had to do the same thing in order to oust Ben. And when Locke arrived back at camp with Cooper's body, the Others suddenly had two viable leaders and they began to split (with Alpert siding with Locke; some followers wanted change).
Locke had failed at becoming the leader of the beach survivors. Locke had more success as the Other's leader until his decision making continued to be wrong. In order to stop the island time skips, he was told that he had to reset the frozen donkey wheel, and to die. Locke never understood the meaning of the latter. His death did not do anything to rally any island inhabitant to change or assume the leadership mantel. He was always considered a weak leader.
Another weak leader was Jacob. He was a sideline leader. The Others worshipped him like a god, which allowed their group leaders like Ben to manipulate people by claiming he had spoken to Jacob and this is what Jacob wanted them to do. But Ben never saw Jacob until the confrontation in the statue with Flocke. Jacob did not want to interact with the humans he brought to the island. Whether it was beneath him, like pets or lab rats to amuse MIB, Jacob was clearly disconnected with the idea of making decisions for other people.
In the same way, Jack did not want to make island decisions. He became the beach camp leader by default, as the survivors saw Jack, the Doctor, as an educated, smart and worthy leader because of his professional skills. He was their immediate best hope for survival from their plane crash injuries, physical and mental. But as the burden of leadership grew with Jack, he tried to make hard decisions but was stunned with the amount of push-back from his fellow survivors, including people like Kate. Jack's role as an island was one of convenience. He did not change the fate of his fellow castaways who slowly were killed off by the island events, including missions he led in the jungle.
Though leadership was a large theme of the series, the role of leader seems to be secondary. There was a large story format of "follow the leader," as in the child's game - - - which could be an explanation of the constant not-well-thought-out mission sequences. Leadership was more a childlike game on the island, possibly because the island was run by a childlike power.
It is possible that leadership was merely a decoy, a ruse, a game of play to keep the island, as a supernatural childlike entity, occupied from tapping its destructive powers that could destroy the entire universe. The island guardian was needed to check the needs and welfare of the island itself, as a living being of vast power, otherwise the island child could go on a cosmic rampage which would destroy all Life on Earth. It is an interesting theory that could have been a light bulb moment for the series if that was the explanation of the show's premise, but sadly it was not the case. The leadership story arcs were merely a tennis match of back and forth power struggles that constitute filler material in the overall story.