Two factors about the Reformed Protestant position back then need to be understood.
(1) They believed in "the priesthood of all believers" - the Bible describes every Christian as part of "a holy priesthood, to offer up spiritual sacrifices, acceptable to God and Jesus Christ... But you are a chosen generation, a royal priesthood, a holy nation; that ye should show forth the praises of him who hath called you out of darkness into his marvellous light. (2 Peter 2:5 & 9) "And hath made us unto our God kings and priests: and we shall reign on the earth," (spoken by the symbolic 24 elders redeemed from the earth, standing before God's throne, Revelation 5:8-10) "...and they shall be priests of God and of Christ, and shall reign with him a thousand years." (Revelation 20:6)
I won't go into that - just point out that their view of "the priesthood" differed radically from that of the Roman Catholics.
(2) The Reformers also considered that the authority of Catholicism in their day had so deteriorated that the Catholic church was "a half-demolished building" (See Calvin's Institutes, IV.2.11) Notre Dame University professor Randall C. Zachman wrote an article with the title, 'Called to Rebuild a Church in Ruins: The Life and Work of John Calvin', for The Expository Times 2014.
Now, I won't go into that either, for we all know that Catholicism ferociously disagreed with the Reformers on those two points. But Martin Luther and others having been put out of the Catholic church, they set about a rebuilding work. Calvin wrote one-third of his massive Institutes on the topic of the Church. See IV.1-3 on "The order of church government as it has been handed down to us from God's pure word", then IV.4 where he examines the history of the early church before the rise of the papacy, and IV.5-13 for how the Roman Catholic Church could no longer be a true church.
Of relevance to the question is Calvin noting that in the early church no one was promoted to the office of presbyter or bishop "without actually undergoing for many years examination under the eyes of the people" (IV.4.10). The people were allowed to choose their own bishops or pastors. "No one was to be thrust into office who was not acceptable to all" (IV.4.11).
Calvin believed that the office of pastor or elder and bishop are one and the same. He emphasized the parity of ministers lest anyone should arrogate to himself the 'sole bishopric' of Christ (IV.2.6). Calvin admitted that there were bishops in the early church, but thought that "the ancient bishops did not intend to fashion any other form of church rule than that which God has laid down in his word" (IV.4.4). Calvin was willing to accept bishops and even archbishops who conformed to the bishops of the early church.
Calvin thought that God "has sometimes at a later period raised up apostles, or at least evangelists in their place, as has happened in our own day" with Luther, "a distinguished apostle of Christ" (IV.3.4).
The Reformers believed that the marks of the true Church were missing in the Catholicism of their day, necessitating the action they took. Calvin wrote about being constrained to "withdraw from them that we might come to Christ" (IV.2.6) Protestants maintained that they were not guilty of schism because what they were leaving was no longer the Church.
Summary: The Reformers considered themselves to be Christians, all of whom are priests in the biblical sense. The men who are to lead Christ's Church are to be godly men, full of the Holy Spirit, and true to the word of God. They set about a rebuilding work which required church order and discipline to be established. That is what they did, including the appointing of other godly men to the various offices of the Church visible.