Then the eleven disciples went away into Galilee, into a mountain where Jesus had appointed them. [Matthew 28:16 KJV]
The eleven had a specific appointment and at that appointment they were instructed :
And Jesus came and spake unto them [Matthew 28:18 KJV]
Jesus spake unto them, that is to say, to the eleven.
And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth. [Matthew 28:18 KJ]
Because all power in heaven and in earth has been given to Jesus Christ, risen from the dead, therefore he says to the eleven :
Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: [Matthew 28:19 KJV]
These words were uttered to the eleven and later another was called, specifically and particularly, by Jesus Christ's audible words, namely Saul of Tarsus, thereafter called Paul.
To him was also given like commandment 'he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel'.
Thereafter a ministry became evident, such as John Mark, Silvanus, Epaphras, Timothy and Titus. Not of the eleven but marked out as a ministry sent to the whole church (not to any specific location) and to propagate the gospel throughout the known world. Paul writes three epistles to this ongoing, next-generation ministry, instructing them in doctrine and in church government. These men, and only these men, may appoint elders.
Here is a definite structure dependent upon the calling, directly, of Jesus Christ. Without that calling, generation by generation, there will be none to 'teach and baptise' among the nations.
One cannot self-appoint oneself to the vocation or to the task.
I can see no evidence here for a 'Great Commission' uttered to the entire church as though the congregations themselves had a 'commandment' as such from the risen and all-powerful Christ.
Quite the opposite, the content of the epistles conveys a godly humility, household-centred Christianity and a very local influence among the parochial populace.
To say 'the Great Commission' is to the entire body of the congregations, to my mind belittles the Ministry - that of teaching and preaching (to the assemblies and also to the whole earth) as a definite vocation to singularly called persons.
Where did this idea come from of a 'Great Commission' which is generic to the entire body of Christ ? I cannot find such words in my bible.
I am asking this question specifically of Trinitarian Protestants as it seems to me that the concept has generated from within that part of Christendom.
The other matter which complicates this issue is what J N Darby called 'the notion of a clergyman ; sin against the Holy Spirit' that is to say the denial of a ministry sent to the entire church and the notion that each local assembly should have its own, private, appointed, salaried clergyman.
But I shall ask another question on that second complication.
EDIT AFTER COMMENTS :
I suggest that there are two aspects. One's local life, home life, church life; and there is the gospel being preached to all creation which is beyond the abilities or capacities of common believers and is the province of the especially called.
Both are true. Both are immediate. Both are essential. Neither should be neglected.
And one should not diminish the other.