For my 12.5 mm playing cue shaft, I use a dime radius on the tip and 12.5 mm is about as large as you can go and still use a dime radius.
If you have a 13 mm shaft and use a dime radius, the edges go down almost to the ferrule. So just a few "re-shapings" of the tip and it is time to install a new tip! And since many new tips "squish" down when first used, you would not get much use out of the tip before it needed replacement.
So the main reason I use a 12.5 mm shaft is to get more use out of my tip before it needs replacement, yet be as large as possible to keep the tip from "squishing" down much. (Tips on smaller shafts will squish down easier.)
For my 13 mm breaking cue, I use a quarter radius tip, so a smaller size is not needed. I also want this tip to be larger so it will not "squish" down as easily. I use a Tiger break/jump tip which seems to be very "squish" resistant.
For my 13 mm jump cue, I use a dime radius tip, but this is a phenolic tip which does not squish and does not need reshaping typically.
I heard that some Masse' cues use a 14 mm tip. I don't know if this is true or not?