Throwing cannon to the wind for the sake of an epic battle is mod territory.
1) The enclave and BoS have deep, long term rivalry. If the BoS now absolutely refuses to even think of being at peace with the institute when they just encountered them, and when the institute have legitimate means to repair the wastes, there is no chance these two would work together.
2) In a certain ending involving the enclave remnants, Lanius sends hundreds of legionaries to destroy them, to nobody surprise sending in primarily melee combatants in football gear to dudes in power armor only achieves raising his soldiers mortality rate. Even without the enclave, the BoS have similar technology (especially since they confiscated their stuff from the Adams AFB at the end of FO3). In addition to having much larger presence and active role in the commonwealth than the east coast brotherhood, never mind those five remnant schmups.
Legion forces would be utterly destroyed, by either faction alone at that.