The Enclave was a Authoritarian Regime ruled by a Oligarchy...their vulnerability was their low numbers and how they had most of their eggs in one basket (the Oil Rig). Richardson couldn't just kill whoever he wanted to, he had to justify his actions to the other power brokers within the Enclave. If they decided his actions didn't benefit the Enclave anymore, they could start the mechanisms of Presidential Succession. CL, as Caesar himself proudly tells you if you ask him, was designed from the ground up as a Totalitarian Regime. All power is vested in Caesar alone, his subordinates are nothing without his power behind them. If he becomes a threat to the Regime's existence, there is no legitimate means of removing him, he has to be deposed by assassination and/or a coup.
Richardson has been the elected President for five terms, I don't really think that there was an Enclave ruling over the Oil Rig, if I'm reading you correctly; in-fact in Fallout 2 whether the Enclave was even the Enclave is debatable. It's not that the Enclave, as in the organisation, is the the legitimate successor to the US, the people within it were; I mean Richardson is the elected President of the United States, not the Enclave. The Enclave, as an organisation, really doesn't exist anymore because it is in it's entirety the population of the official United States. We have no idication as too how it worked pre-war but I have my theories, but regardless, the Enclave itself was obviously never an official organisation within the US system, it organised itself and presumably those within it who wielded the most power, had the most contacts etc, were at the top, if there was even a top. What I'm getting at is that the Oil Rig was ruled by the elected officials because it was the US government in charge, there are no private instituations, no media, no industries, who else could compose an Enclave then aside from government personnel? Besides which the point of an Enclave would be moot because of it's small size and the fact that they are all united in a common purpose, there are no strings to pull from behind the scences, no shady government contracts to slip past the public. Whilst I do imagine that the upper echelons of Oil Rig society were above the propaganda and acted logically; they themselves all believed in the same core principles which have been hammered in through the generations. There are probably strong bonds of unity between the people of the Oil Rig and national spirit.
I don't think Richardson was a dictator, if, again, that is what you were suggesting, why would he kill one of his own people, even if he ever needed too (given the nature of the citizens I doubt he would ever have too). Though he does appear to be above the usual propaganda, or at least realised it for what it was, which I believe can be evidenced by the fact that he talks about how a mutant-Enclave collaberation would eventually fail to them being outnumbered, whereas the rest of the people don't have any reason at all just blind hate. I just can't imagine the regimental society allowing devaints, Navarro seems to have a much more liberal system (which I believe may have been intentional, which is why personnel who don't see what the Enclave was doing as ethical leave.
I guess what I am trying to say is that the idea of the Enclave, as a shadowy, puppet-master organisation, won't have survived or even be understood because of the nature of the organisation, society and passage of time. Unless all of the elections were rigged for the 150 years (which given Eden's ability to become President I doubt) and within the Enclave was a heriditary dictatorship which kept all of the past-knowledge alive, I see no reason why this should be the case or why it would even make sense to do so.