The Christian leaders I’ve associated with have always said they want to be a New Testament church. But usually, they mean they want to be a New Testament congregation. Paul, however, clearly wrote about authority and involvement in multiple congregations. (Of course, maybe you believe that God put things in the Bible that don’t apply to us today).
The New Testament seems to indicate one church in a city, with multiple meetings in homes, and multiple elders. Sometimes outside leaders not only had input into local congregations, they had authority over them. These leaders were sometimes called apostles.

I’m not proposing that congregationalists, such as Baptists and other independent types, give up authority over their own churches lightly. Even their own congregation may not contain anyone who is anointed by God. But I suggest we learn to recognize authority when we see it, and not pretend we have it when we don’t.