I might be making some naive assumptions here, but I have a hard time seeing what the purpose of congregations are in the context of priesthood of all believers.
As I understand it, priesthood of all believers basically says that all people have direct and equal access to God, as well as equal privilege and authority to minister. What then is the purpose of congregating? Why are those congregations well organized?
At least part of this answer I believe comes through obedience to the many ‘one another’ commands of the New Testament.
We are exhorted in various ways to be involved with and caring for one another:
An overview of the Greek 'one another' is given in Christian Fellowship by J. Hampton Keathley, III which states:
The expression ‘one another’ is a translation of a reciprocal pronoun in the Greek New Testament. Reciprocal means mutual, shared, shown or felt alike by both sides, united in feelings, actions, responsibilities, and attitudes. Synonyms include: common, mutual, fellowship, and shared—ideas that are at the heart of the doctrine of fellowship. In usage, this pronoun is used in statements and injunctions to believers regarding shared and mutual responsibilities. In emphasis, it focuses us on our need of the ministry and aid of others, of our duty to care for others as partners in the body of Christ, and of how we can experience true fellowship. Therefore, a study of the ‘one another’ commands of Scripture would be tremendously helpful in the matter of New Testament fellowship. For a detailed study of the doctrine, see the study on the “One Another” Commands of Scripture..
I believe it would be quite hard, if not impossible, to follow these instructions without some form of Congregationalism.
The purpose of congregational gathering is not exclusively to provide the laity access to someone who can be a mediator between them and God, so the assumption that the priesthood of all believers is mutually exclusive is invalid.
Gathering as a congregation has many purposes, including mutual edification, encouragement toward love and good deeds, instruction in the word, serving one another, community, etc.
So, the biblical idea that we all have one Mediator between us and God in no way precludes the call to fellowship with one another.
You are correct in viewing the priesthood of all believers as obviating the need for a mediator between oneself and God - but there is also incumbent upon the participant a duty, as a priest, to minister to one's fellow congregants.
Put simply, without a congregation, there is no one to minister.
As a member in the priesthood of all believers, I am to minister to others in my church, and my church ministers to me. We sharpen, encourage, and build up "the brethren," meaning that we all serve as priests for one another, without respect to hierarchy.
