Having been brought up in a nondenominational church (which shall remain nameless), I have an appreciation for that particular method of church polity. Interestingly, the local church of my formative years was very similar to numerous (thousands, really) other local churches which held to a similar tradition. The ties between these local churches were largely informal, with no central authority or denominational structure to hold them all together.
Each local church, therefore, was responsible for its own finances, discipline, statement of faith, leadership, preachers and teachers, meeting times and places, ministries (e.g., Sunday school, evangelistic outreaches), ad infinitum. In other words, all the local churches had a common historical tradition with a subsequent uniformity of doctrinal beliefs, but with a "schizophrenic" identity as a nondenominational denomination! Let me explain.
Despite the informality of the ties between and among local churches within my "nondenomination," very often two, three, four, or more (sometimes many more) similar churches would band together to take on a project they all could get behind and support. An example of a project might be an evangelistic outreach in the tri-state area or the establishment of a Christian summer camp for kids. My dad was one of the founders of one such camp back in the 1950s, which is still going strong some 60 years later, to the blessing of thousands of young people who came to faith and/or were strengthened in their faith over the decades.
There was tremendous unity among the churches who participated in the camp project, and the camp was staffed and maintained over the years by perhaps seven or eight (or more) local churches through their freewill contributions of time, talent, and treasure. Truly, the camp ministry was a model of cooperation in the accomplishment of an overarching goal of reaching young people for Jesus Christ. Clearly, the camp was a miracle of God!
I could go on to explain how my "nondenomination" had an inordinate--given the relatively small size of our local churches--representation on the mission fields of the world. While on furlough, missionaries who were "commended" by a particular local church to vocational ministry in missions around the world, would "make the rounds" of their "nondenomination," giving updates on their mission work, showing slides (a primitive way of projecting pictures on a special screen, using a projector and tiny pieces of developed film affixed to cardboard squares, called slides), and soliciting prayers and perhaps freewill offerings which could be given to them in person, sent to them directly on the mission field, or even channeled to them through a "nondenominational" mission organization, which functioned as a conduit for monies earmarked for missions and missionaries. We even had a missions magazine which kept local churches informed of what "our" missionaries were doing in Africa, Asia, Europe, the Middle East, Southeast Asia, and so on.
As you can tell, our little "nondenomination" had most--if not all--of the hallmarks of your garden variety denominations (e.g., Baptists, Methodists, Pentecostals, Lutherans, Episcopalians, Roman Catholics, Church of Christ, Church of the Brethren, ad infinitum), except for a central administrative hierarchy to which the denominational churches of our day were (and still are today) accountable. Despite our insistence on our nondenominational status, however, we did many things the denominations did, as I've already indicated, particularly in cooperative efforts in ministry, missions, and stewardship of church-planting funds through a separate but independently run funding corporation (a non-profit 501-C3).
Our insistence on being nondenominational, yet having many of the hallmarks of the denominations, may seem a bit "schizophrenic," and it was. Often when my fellow church members who trumpeted the loudest, "We're not a denomination!" I would think to myself, "Hmmm, the lady doth protest too much!"
Nevertheless, the whole enterprise seemed to work pretty well. Instead of paid ordained pastors or ministers we had volunteer lay preachers and a plurality of elders (and deacons) who exercised servant-leadership in the ongoing affairs of each local church. Years ago there were very few fulltime vocational church workers, save for missionaries who labored elsewhere, and the burdens of maintaining a local church fell to the members of each church. In recent years, I am told, fulltime vocational ministry is becoming increasingly common within my former "nondenomination."
It is quite obvious, then, that God is able to raise up a movement of like-minded brothers and sisters in Christ who have a vision for "doing church" in a slightly different way compared to the bigger denominations, whether they choose to affiliate with other simpatico local churches or not. Any way of "doing church" presents unique challenges, of course, and my little "nondenomination" was not exempt from any of them.
Schisms would crop up from time to time, and the "doctrinal distinctives" which drew us together initially became indistinct and a source of division and disunity within the movement, with subsequent hive-offs and the often hurt feelings and bitterness which accompany such partings of the way.
In conclusion, every local church, no matter how committed it may be to remain independent and thus insulated from the pitfalls of denominational hierarchies and levels of authority (whether presbyteries, bishoprics, governing boards, conferences, denominational headquarters, and the like), can fall prey to the same pitfalls--and more--without a critical mass of committed members who are determined to work together under the leadership of the Holy Spirit and in submission to Christ and to one another to accomplish together what they cannot do separately, no matter how energetic, committed, well endowed, and gifted they might be.
By the way, if you are curious about my current church affiliation, I have been a member of a local Christian and Missionary Alliance church for the last 15 years.