I do agree that a leader must show strength and any organization must have discipline. I do differ to the degrees that such discipline must be maintained and I do not agree with the theory of "culling the weak". With your two island theory, those who are punished for being weak as well as those that are removed from the pool do not work for the whole as hard. Therefore the island, which may not be as strong in discipline, would be able to obtain it's goals that much quicker because they would be willing to spend the effort and time in training and growing their weaker members and therefore making themselves stronger by doing so. Again a strong man is one who is willing to teach and guide a weaker sibling rather than beating them into the ground through harrasment, punishment and death.
Another theory. Assuming that you and I were of equal strength of person and there was only a very weak man that could assist us. Which of us would ultimately be stronger. I because I am willing to teach and help my weaker counterpart and thereby gain his trust, willingness to work and the will to work as hard as he could or you?
I am a seeker of balance. In all ways, the balance must be maintained. A group of people must have a strong leader and must maintain discipline on one hand and at times that leader may need to take strong action that is not always popular. On the other hand though, that leader can make the group more powerful by taking a weaker member and giving of himself, make that weaker member stronger. Even if it is only be a small amount, that change in a person can be significant.
Remember that history has shown that tyrants and dictators are usually overthown. The upheavals though are very seldom done by outside forces but rather are done by internal actions. A tyrant must always watch his back and can never trust his friends. Again which is stronger.
Some thoughts of mine.

Penned by my hand on the 21st of Daedalan, in the year 238 AF.