allow all persons that have worked in both the public and private sectors be allowed to collect both pensions.

Under the current law workers that have worked at least 40 quarters in the private sector can not receive full Social Security payments if they have also earned a state teachers' retirement or have worked for the railroads. This same law does not apply to other government employees.
WHY? Politicians, career military, postal workers and many others can receive compensation from multiple pension sources upon qualifying. Why are certain occupations exempt while others are entitled?
My wife worked for 36 years as a public school teacher, and paid into Social Security for well over 20 years before and during her teaching career. Because she was a teacher, she gets one fifth of the earned Social Security benefits she would have received had she chosen another profession. WHY???