Would be pretty satisfying. Depending on what you break, certain enemies movements and attack patterns change and new weaknesses open up. Maybe even have the broken parts become crafting materials you can loot. Might encourage an interesting kind of gameplay loop where we are encouraged to explore the game world and look for high value targets or public event bosses for the materials you can "shoot off" of them. Maybe they enrage and an encounter is triggered. Just throwing ideas here.
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Now I can’t stop thinking of a crossover between Destiny and Monster Hunter: World. I could see your idea being implemented as a boss mechanic or maybe expand i op n the headless Vex.