Under crisis or perceived pressure, there is obvious distrust in the current system. And the desire for a strong leader comes out of a hope of the decisiveness and concentrated power will allow them to “cut through the red tape” and dislodge entrenched stakeholders preventing change. Additionally, if the political and economic system is really complex and have difficult problems that are very systemic and don’t have clear and immediate causes, this simplifying of the politics to all power being concentrated in an individual becomes desirable (this is Joseph Tainter’s idea that social systems that have become too dysfunctional will create “Caesarism”, his name for desiring a strong man leader).

The other major consideration is that a popular leader that has ties to multiple groups can paper over or avoid conflict between multiple stakeholders or polarized factions in a political system. This is why so much veneration and executive power was given to Washington in the US post-revolution, because that got around a lot of arguments and factional issues between North and South and other colony’s conflicting interests. Both Napolean Bonaparte and Loius Napoleon had this as their main opening for power in the post-Revolution chaos and conflicts in the Second Republic, respectively.