Why do you use phenolphthalein as an indicator in titration of KHP and NaOH?
Because it works.
There are several other indicators we could conceivably use for this titration. Phenolphthalein is cheap, and widely available, and works for the purpose. I always used to like phenolphthalein inasmuch as its acidic form is COLOURLESS, and its endpoint is very recognizable from either direction.
Phenolphthalein is usually used since it is easy to detect visually a slight pink color from a colorless liquid solution.