Tell Bethesda that the BOS can't everywhere, they have the idea that the BOS is a massive organization with resources to spare.
They can't even pacify the Capital Wasteland, yet send a large number of soldiers, technicians, and scientists, not to mention their most important military asset for not much of a reason to a region they know little about.
Not even "because the Institute is there" is a valid reason as the BOS previously barely knew about them, let alone consider them to be an actual military threat.
Also goes the other way, if the BOS had never shown up, had the Institute considered the BOS a threat?