In my basement apartment, I had concrete underlayment and I decided to not install tile under the cabinets even though some people advised me to do. It turned out well especially because I ended up installing 2x4 near on the other side of the front base of the cabinets to screw the front into for extra firmness, which would have been more difficult with tiles. Overall, it worked well, saved me tile and labor to have the cabinets sit directly on the concrete underlayment.
Now I'm doing my upstairs kitchen, which of course is not on a concrete underlayment but on a subfloor stack consisting of 3/4" OSB, 1/2" ply (for extra firmness), 1/4" cementboard, then tile. I intend to again repeat the no tile under cabinet methodology but my question is, since the underlayment is different, should I also skip the 1/4" cementboard under the cabinets? I can see pros and cons both ways. If I did, the countertops would be 1/4" higher, if not, I could save some cementboard.