Vault Tec was contracted by the US government, the Enclave and the government are one and the same, though the post-war Enclave are descendants at best. Whilst Vault Tec were coontracted, it was the US government that had control over the turnout of the Vaults themselves. There is no reason why the Enclave would have deemed Vault Tec valuable enough for post-war preservation.
The Enclave were around before the war, and seperate (but including members of) the government. They were a "Shadow" government
One of the few old world organizations to survive the http://fallout.wikia.com/wiki/Great_War, the Enclave was once the shadow government of the United States. Members of the Enclave both embraced the idea of a nuclear war and knew that the common man could not survive it. They believed that as long as the "important people" of the United States survived, they could regroup quickly and wipe out communism once and for all. Though not technically part of the Enclave, many powerful corporations benefited from the Enclave's actions and their research facilities were protected during the "firestorm" of http://fallout.wikia.com/wiki/Timeline#2077.
Note a "Shadow Government" isnt as creepy as it sounds - it just means that they're sort of an "Alternative" government who sit in the sidelines just in case something happens.... (In Parlementary Government systems we have "Shadow Ministers" who are a part of the opposition parties... Its a similar thing to that, except kinda more official.
Next to vault-tec, Its not neccesarily that they were vaulable enough for post-war preservation.... Lets look at some real world examples of what I mean:
http://en.wikipedia.org/wiki/Air_America_(airline)
Lets assume the rumours here are true: Is this organisation a part of the CIA? Yes, and no.
Vault Tec, being integral to the Enclave's "Project Safehouse" plans would have been under enclave control pre war in order to put a "happy face" onto project safehouse. Project Safehouse, as we all know, would have needed some things that the Enclave wouldnt want folks outside to know - why risk it with an organsiation you dont control?