#K_(sp)# values are usually tabulated for a variety of sparingly soluble and insoluble salts. Of course, this relies on initial measurments (usually by the use of radioisotopes).
Explanation:
You still have to be able to use the #K_(sp)# values in a variety of situations. #PbCl_2# should be more soluble in pure water than in hydrochloric acid. Why should this be so?