blowing up the only place that housed significant scientific technology and data.

The BoS got a shitload of data if we give them the initial network scan. More so if we do their ending (as i'd say Ingram and other scribes took the place apart during our rampage).

Really what did the Institute offer? Some cabbages likely grown with FEV? Synth Gorillas? Three other divisions dedicated to making defective self aware robots and recovering them when they escape. Laser Weapons that are weaker then pre-war models? Oh yeah the molecular relay that requires a hell of allot of resources to keep up and running and probably doesn't seem worth the effort when the BoS already has a large air fleet that can get them around the country much easier.

To clarify I'm just talking about their scientific research. Yeah having a rad-free underground lair is nice but its not like its the only one in the world. For the BoS at least blowing it up would be such a power play, get rid of the Institute plus their Synths and at the same time making the statement, don't fuck with us we just blew the Institute up and we have a giant robot.