The Father ~ Christ~Man
5 For there is one God and one mediator between God and men, the man Christ Jesus,
Sacerdotalism necessitates a priest
The Father ~ Christ~Priest~Man
But, the veil has been torn.
19 Therefore, brothers, since we have confidence to enter the Most Holy Place by the blood of Jesus, 20 by a new and living way opened for us through the curtain, that is, his body
We the elect are the priests.
5 you also, like living stones, are being built into a spiritual house to be a holy priesthood, offering spiritual sacrifices acceptable to God through Jesus Christ.
4 Christ is the end of the law so that there may be righteousness for everyone who believes.
And Jesus the High Priest
24 but because Jesus lives forever, he has a permanent priesthood. 25 Therefore he is able to save completely those who come to God through him, because he always lives to intercede for them.
Sacerdotalism in my view insulates people from God, where the New Testament places none.