The topic here is where you agree/disagree and your thoughts. I wasn't really sure how to present this thread. So let me explain how I feel about these things.
Enclave: They wanted to cleanse the world of the radiation that has stricken it. They failed in the sense many of the superiors considered all people that weren't in the enclave's bunkers during the bombs being dropped are not worth saving. As if the evolution (not in a good way mind you) of the human race to adapt to radiation, or mesh radiation, was not worth saving. This left literally everyone their enemy. They did have a very strong hold due to their advancements in technology. However, the actions of the antagonists of F1-F3 destroyed them.
In Fallout 1, their headquarters off the coast of California was destroyed.
In Fallout 2, another one of their largest bases was destroyed.
In Fallout 3, another one was destroyed, along with a supercomputer ZAX personality that essentially solved the problems that wound so many civilizations. Leadership, and how people react to the leader changing.
Brotherhood of Steel: In the war of 2077, humanity had lost much of it's progress. The BoS wanted to recover as much of the past as they could, so that the future could speed it's progress. Einstein said that he did not know what World War 3 would be fought with, but knew that World War 4 would be fought with sticks and stones. The BoS aimed to recover the weapons of world war 3, essentially. Their fall was in their primitive form of leadership and government. The only people that were allowed to be BoS were people that were born into it. From what I've seen however, a couple locations of BoS corrected this within themselves. Like in Tactics and F3.
In New Vegas, when you approach the Brotherhood of Steel, you are held at gunpoint right upon discovering the outskirts of their establishment. Everyone refers to you as outsider, and you have little to no respect. Mr. House commented about 4 of the bunkers self destruction upon them being invaded. He commented about their unwillingness to compromise. Much of their faction is rooted in tradition, and cares little about humanity. This is exemplified within the Outcasts. They did not want to help squabbling wastelanders, and decided to break off to get back to the main goal. Recover technology and reverse engineer it for future use.
New California Republic: NCR is the group that I have the least to speak about on what they did wrong. From the start, they did a lot right. They chose a democratic leadership which means the people are in power. At this early in their existence (less than 200 years.) and the fact that they are still of course in a wasteland, cheating and propaganda isn't as prominent.
However, they often fail in their very virtues. As one president's reign over 50 years. Caesar has commented on such. He said he respected the president Aaron Kimball but thinks the NCR would have done better if he seized power rather than "earned" it. This of course is paraphrased. Their downfalls are that they are widely spread out, and sort of backhand their way into areas. They are not forceful like the legion, but none the less take control of whatever area they seek to occupy. Which is why House had a problem with them.
The large majority of their troops are green. They are new and untrained. If you ever worked for the NCR in New Vegas, you will find out there is a lot of shady business, and even one of the captains is a legion Frumentariis. The largeness of the group makes them very vulnerable to such things.
Caesar's Legion: From the start, the Legion was a brutal, ruthless, and dominant group. Their numbers are largely bolstered by conquering tribes. Caesar is thus known as the conquerer of 86 tribes. Many of his highest ranking members (Legate Lanius) came from conquered tribes. Im reluctant to reference Lanius, as his existence is largely shrouded in mystery, and there is much speculation that Lanius is merely a name and a mask. Kinda like when Captain America was frozen in the iceberg and his friend took over the role (Sorry, Im a geek ).
What Caesar and his legion did right was that no outsiders could merely earn their membership. You came in by being conquered and young enough to be swayed into a legionnaire. The members are taught to be fiercely loyal to their leader Caesar. The unusable in the ones they conquer are made into slaves. Further making use of the conquered. They are ruthless, show no mercy, and even commit suicide on imminent defeat so they cannot be interrogated.
The reason they will eventually fall is best expressed through the words of others. The Legionnaires follow Caesar and his rule, not his ideals. Human nature always conquers every government that tries to oppose it. Which is why communism constantly fails in the real world. When Caesar falls there is much pointing to the falling of the legion. They are made to lead one leader, a constant leader, an emperor. The very faction is named after one person. What happens when he dies of old age? Infighting will eventually topple CL.
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In conclusion, there is only one faction who did basically everything right.
So may I finish this off properly by saying this; TUNNEL SNAKES RULE