That's pretty sweet. I've seen it happen occasionally on several different trees. But I've never seen it happen a lot on any one tree. I don't have Kadota so I can't compare.

In your Zone 9 it will ripen all of them.
In cold climate ,it will only get ripe a few,most others,drying out and die without getting ripe.

Of course the quality of fruits,will improve if ,part of crop is removed.
Also the tree will be health yer if done,but that is up to you.