It seems that no resource I come across addresses the fact that the pH range for phenolphthalein's color change is around 8.2-10. In other words, it's still colorless at 8.2. Why then, is it claimed that the indicator changes colors when the solution changes from an acid to a base? Wouldn't you want an indicator that changes colors at about pH 7?
If you analyse a titration curve you will immediately notice the pH shooting up near equivalence point. For this reason, there is very little difference to the amount of base added for pH 7 and pH 8 (due to the logarithmic nature of pH). So, it's not entirely accurate but certainly good enough (for strong acid - strong base and weak acid - strong base), if you want something better use an electronic pH tester
In order to determine what indicator to use, you have to identify the reactants and strong or weak. For a strong base and strong acid reaction the pH shift will likely occur around 7. If its a strong acid vs a weak base, then the pH will probably lower than 7.