The classic "It's a fantasy world so it doesn't need to have consistency" defense. Do people still use that unironically? Isn't that kind of an automatic L in any discussion?
Vault-tec wasn't a wing of the Enclave, also the Enclave didn't control the FEV and they weren't just "The Government" they were more a group of elites that included military personell, rich corporates, government officials and the like, they were more the "Deep State" than the government controlling everything. Vault-tec didn't even have anything to do with the FEV to begin with. The Super Mutants weren't the end project of the FEV experiment and they only came about after decades of experimentation by the Master, and he created them with a propouse. Now, because bethesda has the imagination of a teenager on anti-hyperactivity drugs they need to convolute new ways for there being a increasingly numerous amounts of what in the first game was explictly a freak discovery of a Mutated genius madman, and they also increasingly forget to give their existence a porpouse. You know, text book Shitty writing. Fanfic level.
In FO1: A man falls into vats of the FEV and after years of mutating and combining with other living creatures he emerges as the Master. He then starts experiments to see how the FEV could be used to help humanity survive and his most promising project is the Super Mutants, but even he doesn't know how to make them properly and comes to the conclussion that proper Super Mutants would be the result of using "pure humans" from Vaults as the base.
FO2: The Enclave after hearing about the debacle of the Unity and it's destruction, launches an expedition to find the FEV so they can experiment with it. To this end they use miners from Reddin to excavate the rubble, in a freak accident, several miners fall into the Vats, creating the Second generation super mutants. The Enclave later experiments with the FEV to create Frank Horrigan and the strand of the virus they will use to kill the inland population of the US with the exception of Vault Dwellers and the Enclave themselves.
FO3: This Vault had FEV and they tested it on it's population, even after the war, no idea what their end goal was but they created the Simpsons Super Mutants.
FO4: The Institute got FEV and created Super Mutants for ????? then released them into the surface for ????????
FO76: There was this place that had FEV and they threw it into the water for ?????? it somehow created super mutants despite the fact that those have to be Dipped in the stuff, not drinking it.