Actually, they destroyed University Point because they sent an envoy there to buy the data, and the girl who had the data lied about having it, stalled them for weeks, then tried to go behind their back and sell the data to someone else. And the data at UP wasn't for a gun, it was reactor efficiency data, something they needed to complete phase 3. The gun was an entierly different project unrelated to the data they were trying to buy.
Also, the CPG wasn't The Institute's fault. In fact, they spent 4 years trying to keep the CPG together. The CPG fell apart due to infighting among the various representatives, The Institute got blamed later because they were the weird outsiders, and because the synth was likely the last one sanding due to being a robot.