In my answer to your similar question I cited R. Saadiah Gaon (Emunot V'Deiot 3:9) who wrote:
The third [problem is presented by] the fact that God commanded all men to offer up sacrifices and then forbade such activities to everyone except Aaron and his children. But this, too, did not constitute an abrogation, for there is not contained in Scripture a single text indicating that all men had been appointed to perform the sacrificial rite. Before the appointment of Aaron it was only who had been appointed to a position similar to his that performed this rite. One who had not been appointed, however, had no right to engage in the performance of the sacrificial rite, neither before nor after the election of Aaron.
(Rosenblatt translation p. 168-19)
If this is true with regard to sacrificial offerings it may well be true with regard to other functions of the priesthood as well.