The way I look at it is, why wouldn't you core? I used to be a huge opponent to coring. Didn't believe in it because like mentioned I wanted my cues to hit like the woods I used. But something happened that changed my mind. I got good enough that all my cues hit the same, anyway, regardless of woods used. I choose & match wood according to tone in order to achieve a specific tone that I believe is best for playability. Once I got good at finding that tone, everything began hitting the same. So that brought me to question whether to core, or not to core.
Reasons to core include much higher confidence in stability, easier weight & balance control, added strength to weak or highly figured woods, manipulating(enhancing) tonal qualities in otherwise crappy tone woods, and the ability to successfully use nearly any wood imaginable.
Reasons not to core.......I dunno. Got no reasons anymore.
So the choice was easy for me. I took my abilities & skills as far as I could without coring and in order to further advance, I had to start doing it. It opened an entirely new & exciting realm of possibilities in my cues. I can core with different types of wood to achieve a desired weight & tone. I can use ultra strong & stiff woods to core softer & more flexible woods. I can take it even further by varying the size of the cores. It's a science. I'm still learning but I can say for certain that i'll never go back to not coring. I used to argue against coring and at that time, coring was not a benefit to me. Now i'm at a different level & coring is now a critical step in my cues. My techniques change with my knowledge & ability level. So for me personally at my level, coring is essential. 5 years ago, coring was not of any help to me because there were lots of things I still had to learn & never would have learned it if I had bypassed it with coring. Hopefully this makes sense & helps you figure out your own situation.