Customizing your cohort is just a simple solution for lazy DMs, From what I understand, a Cohort is an NPC you've convinced to follow you, whatever which way. So the DM should create some sort of System for the player to acquire a cohort, such as a quest, or the NPC witnessed the Player in action and followed him in awe. In my Kingmaker Campaign, we run into a lot of people, whom I've chosen to demand Fealty rather than kill, and as such, When I pick up leadership, I'm going to choose one of my followers and promote them to Cohort.
Leadership is broken due to the laziness of the DM, you Fix it by not being lazy, done and done.