The distinction between elected and appointed positions is hardwired into the Constitution. This distinction arises in many contexts: the Foreign Emoluments Clause, Section 3, and now the qualifications for the Senate.
Article I, Section 3, lists three qualifications to serve in the Senate:
No Person shall be a Senator who shall not have (i) attained to the Age of thirty Years, and (ii) been nine Years a Citizen of the United States, and (iii) who shall not, when elected, be an Inhabitant of that State for which he shall be chosen.
