I core only the woods I feel need it, such as burls. Everything else is uncored. Nothing wrong with coring, so long as the builder & buyer are both satisfied. Nothing wrong with not coring, so long as builder & buyer are both satisfied.
Pros of coring are consistency of hit from cue to cue, which I find easy enough to do without coring. Next is stability, less likeliness of warpage, which I find easy enough to do without coring. Easier method of controlling weight, especially with heavy woods, and again I do it without coring. That's about it. It's not right, not wrong, just different strokes for different folks. We all have our own methods & those methods are chosen because it works for us.
My freind, Wes Hunter, and myself live in the same area & share many materials, ideas, techniques, etc. He builds his cues with cored forearms & cored handles, using fantastic wood as cores. His cues hit superb & are second to none in quality. I, on the other hand, do not core anything except burls. I also build what I feel are very nice cues that play top notch. Aside from coring, he & I use the same materials such as woods & phenolics. The butts of our cues are dimensionally very similar with mine being .850"x1.25" & his being .845"x1.25". Our shaft tapers are different but we use the same shaft wood. Our ferrule install technique is different but we use the same material. Our cues both come out solid & stable players with slight playability & feel differences due to shaft taper & tip choice. Again, he cores & I do not. That's a pretty close comparison of two cues with different core beleifs, and both cues are good cues.
In the end, it comes down to the builder's beleifs & preferences. The end result is a cue that is solid & sound, no matter which method was used to construct it. If it's well built, it's well built. The cueball won't know the difference in how it was constructed. You as a player likely will not know the difference, and if you do it is not a difference that defines good or bad.
I could go on about why I don't core my cues, but there's no reason to. My personal feelings & beleifs mean little or nothing when two guys match up & one has my cue & the other has Wes' cue. Both are good cues, one cored & one not, so it'll be the better player that wins & not the cue. I often play one hole with Wes & the results are mixed, with each of us winning and losing by how we play. I can & have played well with his cored cues. So my point of this rambling is that there are no true pros or cons to coring, in my opinion. It falls into the matter of the builder's preference of construction techniques. But matters nothing when the tip touches the cueball.