They are taught to hate mainland mutants and such, presuamably to make the Project seem less un-ethical and even a good thing, not just a necessacity, whilst they are genetically different. It is also for political reasons, it would be impossible for the Enclave to establish law and order across the mainland and nobody respects their authority anyway; as far as they were concerned, starting again was the only reasonable course of action.
Agreed.
The Enclave has one main function, to restore America to it's former glory. Frankly, this is impossible in the current apocalyptic situation. With mutants, ghouls, and other mutated beings running amok, the Enclave has to figure out a way to deal with this. Thus they chose to take the plan that involved less potential human casualties on their side: a plan to saturate the air with a FEV-based chemical that would wipe out the entire local population. While I agree that this may not be the most ethical way to deal with it, you have to look at this from a numerical standpoint. The Enclave, while numerically and technologically strong, has limited recruits and personnel compared to the number of mutants out there in the wasteland. This includes any super mutant, ghoul, raider, radscorpion, and any human-populated faction out there, (with the exception of some BoS factions). If they were to actually send out their troops on a mission to wipe out any form of irradiation, there would be limited success. This would include using the limited number of Vertibirds (remember, they could only maintain Vertibirds, not create them) and fuel (this was especially limited) they have, precious pure human personnel, and expensive Power Armor and equipment. That's why in both the Western (Oil Rig) Enclave and Eastern (Raven Rock) Enclave, they chose to take the plan where they could sit back and take the region over after the FEV virus had eliminated most of the resistance. Of course, this is where Black Isle and Bethesda introduce a hero that cannot join the Enclave, but rather wipes them out in their respective regions. The Chosen One and the 101 Hero both have what I would call "protagonist immunity", where all of the well-prepared and organized fortifications and forces they had that took countless years to build were destroyed in a few hours by one guy and a few of his companions. That's why I really hope in a future DLC or game that there will be a chance to see a growing Enclave faction, and actually join them than be forced with the decision to annihilate them.
In comparison, other powerful factions of the Fallout universe are much more weak when compared to the Enclave. The BoS (which was originally a small group of soldiers and their families rebelling against the government) is equally reclusive and somewhat technologically advanced as the Enclave. However, the Enclave, given time, would make much more progress than the BoS ever would. If you compared the Mojave chapter of the BoS to the Enclave, you could see the difference. In the Mojave chapter, you saw a BoS faction, that was busy following a obviously deranged Elder (Elijah) that was leading them to imminent doom by focusing on the little situations rather than the big one. Elijah chose to focus on a single structure that, while housing a super weapon, could have been captured in the much easier after building a successful strategy. Instead, he chose to waste previous Paladins and Initiates, throwing them against the NCR forces until he was able to extract some technological data (which of course he never acquired) that the NCR would have never possibly been able to even access given their lack of technology and competent engineers and researchers. Elder McNamara was no different, as he chose to retreat the BoS to a location that was essentially, right next door to where they were defeated. He chose to hide in recluse for an unreasonable long amount of time next door to his enemy while he could of simply used the Hidden Valley as a temporary shelter, and move out in the night when the NCR would have a harder time tracking them. He could have very well relocated to a much further location where a NCR presence was much lower. In comparison, look at Richardson's Enclave. While they were reclusive as well, they weren't as hiding as they were growing. Richardson had a huge force, ranging from the super human Frank Horrigan to the armada of troops in Power Armor and plasma weapons he had at his disposal. Richardson chose to pick his battles wisely, and chose only specific targets that were low-attention to other warring factions, such as Arroyo (of course, this is where the Chosen One, the player, had to come in a destroy everything no matter if they wanted to join the Enclave or not).
The NCR as well, is just as weak when put next to the Enclave. While they do hold the numerical advantage, they lack the sufficient technology on par with other high-tech factions. While they are definitely rapidly growing, the government in which is the foundation of the Republic has alrady been corrupted. The NCR is now run by a group of politicians who know nothing of how to run a nation. One such politician would be Kimball, who turned an originally steadily growing nation of power and technology under Tandi, into a imperialistic-like nation that over extends it's borders and regions and spreads it's troops out too thinly (examples in the real world of this would be the former British Empire, the WW2-Era Japan, and the Napoleonic France, and we saw the success of those nations). While certainly powerful, the NCR is already weak internally, and thus cannot truly grow into a powerful faction as the Enclave. Compared to Richardson, Kimball would be something short of a moron. Richardson had one goal, and that was to better the future America that was the Enclave. Rather than focusing on his own personal fortune or fate, he lead the Enclave to a stronger and much more strengthened faction. This is why the Enclave essentially kicks the ass of any other faction out there.
On the topic of remaining forces and bases, the Enclave still could have much hidden away in the huge expanse of America. We still haven't seen any post-war recognition of Alaska or Canada, two areas that the Enclave could have surely used as for military bases. In addition, Chicago has been explicitly stated, so there must be a significant force there. With Enclave personnel retreating from bases such as Raven Rock and the Mobile Base Crawler, we could see Chicago turn into a powerful location for the Enclave to rebuild. Also, much of the rest of the US has still yet to be mentioned yet. Regions such as Florida, Texas, Washington, Vermont, Delaware, and North Dakota have yet to be fully introduced, and there is most likely numerous Vaults there, as well as an Enclave presence.