This eliminates you as a potential threat and you have no chance to use other limited resources outside of that system.
You might be able to produce some nasty radiation/ionized crap/relativistic debris that would be unpleasant for that greenish scum clinging to some of the planets, but it'd be a really expensive way to do even that.
Sure, if you get close enough to C, you can deliver as much energy as you want, but you're probably going to use the energy of several stars to get a small object going fast enough to deposit a really destructive amount of energy into a single star.
Efficiency is part of finesse...
personally I'd go for something like a nanobot gray goo thing that infects & turns everything it touches in a given gravity well. then send over a bunch of ships to wipe out remaining stragglers.