I've never bothered to find out my cue's pivot point, and I don't think I need to learn where it is. I've probably found it unconsciously through years of shooting with it. It's not something I want to know consciously because it'll be just one more thing I'll have to think about when I shoot. I want to limit the things I think about while shooting, and I doubt that the pivot point is anywhere near important enough to add to my list of thoughts I rank as being necessary.
There gets to be a point where too much "knowledge" can destroy a person's pre-shot, shot, and post-shot routines. I don't want to think about dominant eye (which is another thing I think is BS), backhand english, dropping or not dropping the elbow, squirt, etc. I concentrate on the contact point and that's it. I was a baseball pitcher for a long time, and there's a difference between AIMING at the mitt and THROWING at the mitt. Too many thoughts lead to AIMING at the mitt. I apply the same thinking to pool. I try to leave out all extraneous thought and concentrate on that mitt (contact point). I try to allow my body to do what comes naturally - I don't want to force or control any muscles or thoughts. When I threw a baseball, I didn't think about humidity, temperature, sea level, variations in ball weight, grip pressure, etc. I just threw the damn ball. Why can't pool players just shoot?
So I guess in answer to your questions, pivot point doesn't factor at all in my decision to play with my cue. The other things you mention (balance point, taper, etc.) are all far more important to me. Plus, I've played with my cue for so long that I don't think I'll ever want to change. I don't buy all the technology crap that promises to make your game better (they don't - heart, desire, and pride make your game better). I don't need a cue with super-exotic wood costing tens of thousands of dollars. My cue is my comfortable pair of old jeans - sure, there are better looking, more expensive jeans out there, but none are gonna feel like those old jeans.
-djb