Though I cannot give you chapter and verse from Luther's writings that prove that he rejected sacerdotalism and accepted the "priesthood of all believers" in its place, I can (and will) refer you to key verses in both Testaments that may have been influential in Luther's rejection of sacerdotalism.
First, the idea of the priesthood of all believers originates in Exodus 19, where God told Moses from the "mountain of God" in the Sinai,
Now if you obey me fully and keep my covenant, then out of all nations
you will be my treasured possession. Although the whole earth is mine,
you[a] will be for me a kingdom of priests and a holy nation.’ These
are the words you are to speak to the Israelites (vss. 5-6 NIV).
Just as God's vision for the Israelites was for them to be a kingdom of priests and a holy nation, so also God has a vision for the Church of Jesus Christ, being a kingdom of priests:
But you are a chosen people, a royal priesthood, a holy nation, God’s
special possession, that you may declare the praises of him who called
you out of darkness into his wonderful light (1 Peter 2:9 NIV).
And
John,
To the seven churches in the province of Asia:
Grace and peace to you from him who is, and who was, and who is to
come, and from the seven spirits[a] before his throne, and from Jesus
Christ, who is the faithful witness, the firstborn from the dead, and
the ruler of the kings of the earth.
To him who loves us and has freed us from our sins by his blood, and
has made us to be a kingdom and priests to serve his God and Father—to
him be glory and power forever and ever! Amen (Revelation 1:4-6 NIV, my bolding).
Just as Jesus fulfilled the three roles of prophet, priest, and king, so also the Church of Christ worldwide fulfills the roles of prophet, priest, and king (but not individually, but as a kingdom of priests to their God).
Finally, Luther may have taken to heart the words of Paul in 1 Timothy Chapter 2:
I urge, then, first of all, that petitions, prayers, intercession,
and thanksgiving be made for all people—for kings and all those in
authority, that we may live peaceful and quiet lives in all godliness
and holiness. This is good and pleases God our Savior, who wants all
people to be saved and to come to a knowledge of the truth. For there
is one God and one mediator between God and mankind, the man
Christ Jesus, who gave himself as a ransom for all people (vss. 1-6a
NIV, my bolding).
While I would be the last person to say that pastors, rectors, priests, ministers, vicars, clergymen, parsons, clerics, and any other person, male or female, who serve a local church in a clerical or lay role, do not have the privilege and responsibility to pray for members of their congregations. I believe, as did Luther, that to pray for someone is not to act as a mediator between them and God, since there is only one mediator, and that is Jesus Christ.
Mediatorship falls to Jesus, and Jesus alone. Only through Jesus do believers have access to the Father, as Hebrews Chapter 10 makes eminently clear:
Therefore, brothers and sisters, since we have confidence to enter the Most Holy Place by the blood of Jesus, by a new and living way opened for us through the curtain, that is, his body, and since we have a great priest over the house of God, let us draw near to God with a sincere heart and with the full assurance that faith brings, having our hearts sprinkled to cleanse us from a guilty conscience and having our bodies washed with pure water (vss. 19-22 NIV, my bolding).
