Those shards you have... Without boring you with the details, the shards can be used at the monument to empower the Bastion, allowing it to provide buildings, natural structures, magic items - really, you name it. The cores - like that large one - do much larger things.

Beyond the value of using them, there's the fact that you'd have a large number of people of various experiences backing you up, giving you a safe lair from which to go out into the Skyway and hunt without needing worry for your base. As far as we know, we're almost all that remains of our worlds - banding together really is our best hope of survival, as a result.