Someone despised by everyone can come into power when they are born into it. King John of England is a common example, though I don't know how historically accurate.
That said, your point is important and something many people don't seem to understand: those foreign leaders we in the West like to describe as tyrants, dictators, despots, strongmen, etc, are generally at least popular at home, and often adored.
I don't really accept King John as a counter example. I'd revise my statement above to clarify that only someone with popular support can usurp power - unpopular monarchy can inherit power either because (1) the monarchy as an institution is more regarded than individual monarchs (2) once seizing power a tyrant can usually reduce their popular support and retain that power - the same holds for institutions of power, so the monarchy might not be popular but enough power is gained from and invested in it's continuance that no one wants it to go away[1]. John also may have been a desirable monarch because he was initially a useful idiot and managed to ride luck to transform that initial investiture of some power into a stronger reign.
Lastly, popular support is from the factions, not the people - in medieval europe most of the people had no factional representation politically, all the power had been entirely concentrated in the various estates.
1. See Lord Vetinari in like every discworld book ever.
That said, your point is important and something many people don't seem to understand: those foreign leaders we in the West like to describe as tyrants, dictators, despots, strongmen, etc, are generally at least popular at home, and often adored.