Basically, they relocated because Eden said so. Seems like classic bullshit Beth writing.
Yeah, because it also doesn't make any sense; no presidential elections were held. Nor John Henry Eden was in the staff as a legitimate successor. It feels more like a far yell to the Shi, rather than the Enclave. Perhaps, simply, the remnants were following Autumn, and not the president anymore, since the events from the Oil Rig.
I also don't see why the Enclave would create propaganda like it did in Fallout 3. What was the point? The Enclave, especially those under Autumn surely wouldn't take up on any wastelander due to their credo. The masses in the wasteland are also more or less adapted to the post-war environment nor the promises he makes have any direct value.
What does the America of legend mean to someone in the wasteland? When their main need is the one of food, shelter and safety. There are many more important basic needs to be met, before talking about supremacy (against who, anyway? The mutants? The Brotherhood? The Chinese remnants?)
If the strategy was to create a less equipped, but a force that relied on cheap cannon fodder then it would make sense to spread propaganda, take in some raw recruits and make them meat shield against whatever enemy may show up while providing a false promise that they are doing it for America.
What's hard at doing that? There are people all over the wastelands, the people in Vault 101 could also have been taken as cannon fodder (that is already a better idea than simply wasting human talent for FEV) that kind of strategy would further establish the power that the Enclave would seek.
Perhaps, however, if the Enclave was more intelligent then compared to the geniuses that populate the Capital Wasteland then it would make any sort of ending too unrealistic or evil as the Enclave would either be destroyed by less intriguing factions, or just plainly massacres everyone and takes over by forming a socialist state between the elite and the masses who rely on them.
That scenario would also make more sense with the Water Purifier. Why would you want to kill everything in the Wasteland when it already wasn't a good idea when it was attempted all the way to the other side of the coast will all sorts of resources available to the Enclave? Was that not in the equation when John Henry Eden developed consciousness?
Actually, Autumn had the right idea all along. It doesn't make any sense that his forces were to follow an unconstitutional president that was never in the staff over an officer under the ex-president that has more in his mind than some stupid decision making that was done in the Core Region.
It feels forced, and disappointing. So, you are probably right.