We took over the place, depending on the speech check we also disabled most of the Institute's synths stopping them from fighting back and this place, despite having the whole synth thing, has a lot of technology that would be useful for the BoS especially since through certain references the East Coast BoS seems more like a country (One member even literally calling it a country) then a organization.
So anyway the BoS quest ends with the BoS taking over the center of the Institute, killing everything that gets in their way and depending on speech check or hacking abilities shutting down the Synths through Shaun's terminal AND reinforcements have just arrived. Why did we blow it up? The place would be a haven for any BoS member, it's filled with literally everything the BoS strive to get and we just blow it up? In these walls is a way to feed an entire army, to fix Prydwen's energy problems, a way to efficiently teleport soldiers throughout the commonwealth and something that could end the super mutant and feral problems as well as trace down synths is right here. So why did we blow it up? It was literally in our palm, we occupied it, we controlled the entire place and had the manpower to fully occupy and set up a garrison there. Hell, it could've even become the BoS's main base of operations in the Commonwealth but for some reason we just blow it up???
I'm sorry that's kinda lazy writing and doesn't make sense, even for someone as filled with hate for the Institute as Maxson he wouldn't look passed the technological treasure trove that is the Institute.