Non-denominational churches amount to a micro-denomination. There basically is no such thing as non-denominational. With as many denominations as exist, certainly every conceivable interpretation of Scripture is covered. In fact, we probably have way too many denominations. While it is easy to say we should just do away with all denominations, and on some level this is true, how do we resolve some of the most basic differences? If you believe in OSAS, are you willing to then join a newly minted single denomination that rejects OSAS? If you believe in Free Will, would you abandon that belief and embrace Sovereignty? Don't give me the line about relying on Scripture because EVERY denomination relies on Scripture, we all just have a different opinion on how to interpret that. Every non-denominational church does the same exact thing. They HAVE a denomination (in some cases a denomination of exactly one church), they just don't name it or associate with a larger group. That's fine and dandy. I certainly am not bothered by pretty much any denomination that recognizes the core beliefs that we all agree upon (with some notable cultish exceptions). But, we shouldn't be deluded into thinking that non-denominational churches provide unity in any way. They are, if anything, MORE segregated because they have little to no interaction with the core Christian communities. That's their choice, right, wrong, or indifferent, but I fail to see how they are in any way more unified given that they rarely ever associate with any other groups (There is one awesome example in my community that has several non-denomination churches, and a few denominational church doing Bible studies together).
In the end, if a church preaches the Gospel and answers the Great Commission, reaches out to the community and to the world with missions, and displays the love the Jesus shared with the World, then I simply don't care what they call themselves. They are Christians. There will be people in their church that are both going to Heaven, and there will most likely be people who are hypocrites.
So, true, there probably shouldn't be denominations. They have been used for division rather than unity, but I don't think that denominations are the problem. People are the problem. People have used denominations to segregate rather than unify. Denominations allow us to believe what we believe, but to recognize brothers and sisters who don't agree with every detail. Unfortunately, some have allowed their differences to define their relationships. I'm pretty positive that if denominations were done away with and we all rejoined the Catholic Church (which ultimately is what elimination denominations implies), that people would still be just as divided.