At one point, somebody in T1 was able to eliminate the Capitalist faction entirely by killing ANYBODY who even had a shread of sympathy towards Capitalism. He did it at the begining of the game, so as to reduce the amount of killing he had to do (and thus reduce the amount of hatred that would occur as a result). Even then, I believe the Capitalist Faction still had a leader, it's just that a leader that has been dead for quite some time.
The North Korean strategy I was trying to do for my LP of Tropico was partially based on the idea of killing anybody who opposed the regime, but it failed on account of me not building any police station to deal with the military I'm so heavily reliant on killing.
The Paradise Island's Fear mechanic, by the way, only works for elections (as it should, it provides a benieft for actually killing your opponent). There are other ways of losing office, you know. And if you really had any trouble with elections, you should have picked the "Bought the Election" trait, and thus be able to more easily commit election fraud. Without the trait, you can sway 20% of the vote. With Bought the Election, you can sway 30% of the vote, meaning that you'll only need to have the support of 21% of the population in order to win democratic elections.
EDIT: Rakonas: Killing faction leaders always leads to the faction choosing a new leader. However, in T1, killing a competent faction leader leads to a new faction leader who may be more cowardly, have less leadership skill, and might like El Presidente more.
One interesting thing in T1 is that you could easily make factions love you if you just pamper their Faction Leaders with bribes, houses, and lovely jobs.