Part of the problem of keeping few worlds in core alive (aside from pirates) is they are highly vulnerable to pirate raids. In case of indies, they are small, and if you do not defend them from non-stop pirate raids, they will decivilize on their own.
The main reason for me to kill all of the core worlds is to eliminate the babysitting. Spending most of my playtime chasing pirates because core worlds cannot defend themselves, not to mention the core worlds thank me by sending their gigantic invasion fleets at my colonies (which means more time wasted either defending my colonies and/or grinding up rep), is plenty of incentive to kill-'em-all. If I sat bomb worlds, the indies turn hostile, and rather grind rep back up (not to mention I do not want to babysit them), they join the hitlist with the major factions as enemies to be destroyed too for getting in the way. Indies should not turn hostile due to "atrocities" unless they were hit directly.
At first, I wanted to kill all of the core worlds because I wanted my character to be either the evil overlord who kills all opposition then rules the whole sector with an iron fist, or the omnicidal maniac who wants to destroy everything. Now, my character is simply a space settler who wants to be left alone in the wilderness minding is own business of living life, but gets eventually fed up with the constant bullying and will make it stop by any means necessary (which means total core kill).