Imagine if you will, two very influential non-Christians in first century Asia talking about the Nicolaitan philosophy and one asking, "What does the 'Church of Christ' believe about it?" The other says, "Let's find out." So they contact a leader of the church in Pergamos and he says, "Yes, we believe that doctrine." (See Revelation 2:15). They then begin to spread the word that this is what the "Church of Christ" believes about the Nicolaitan doctrine. But, imagine you are a member of the Ephesus church of Christ and you hear that? You hate the Nicolaitan doctrine (see Rev. 2:6). What the Pergamos church of Christ believed or practiced did not hold true for all churches of Christ.
In the first century, the independence of all churches of Christ made it such that, though there were many similarities, things done the same in all the churches, you could not make a broad sweeping statement that ALL churches of Christ believe this, or practice that, for they sometimes did not. The Lord's arrangement of congregational autonomy made such impossible and I might add, it was intended that way by God. Denomination "X" can make a broad statement of faith for all it's churches and likewise denominations "Y" and "Z", but churches of Christ following the original New Testament pattern are not denominational and are therefore unable, and should be unwilling to do so.