Covenant Theology and Dispensationalism are usually presented as two conservative approaches to interpretation of the Bible. Let me give you the cliffs notes on the subject.
We've got the New Testament, inspired by God. What God said is the only right way. That way was persecuted severely by the Roman empire. Doctrine changed out of fear of death and desire for survival. Leaders played loose with the New Testament text out of compromise. You can read this in the patristics, materials that endured with state church sanction. Finally, the Roman empire hijacked Christianity with a distorted form. Roman Catholicism embraced an allegorical interpretation of Scripture in fitting with hierarchical organization. The authorities could tell you what the Bible both was and meant. You couldn't question that because God is the author of all authority and they happen to be the authority by Divine right. Amillennialism became the approved thought about the kingdom. Roman Catholicism could then be as much as the kingdom, and because of its hierarchy, it needed no basis for that position. Ergo, Dark Ages.
We jump to the Reformation. The crusades, the renaissance, and the printing press became the perfect storm for something more and different. Squalor would become unacceptable. Out came sole scriptura. It's got to be in Scripture. We've got our own copy now. Well, amillennialism isn't in, um, the Bible. Religious brains, sympathetic to Catholic style hierarchy, got together and came up with covenant theology as a means of defending amillennialism from the Bible. Amillennialism isn't in the Bible, so more allegory, more spiritualizing, essentially more of the same that led to Roman Catholicism in the first place, had to occur to read amillennialism in there. The Bible, of course, is the casualty in this. No biggie. This continues everything along the subjective approach to Scripture.
With subjectivity the means of operation, a lot of disagreement. State church will solve that for awhile. When there isn't a state church, where everyone is operating according to the same creed, however, lots of theological battles will ensue. People can take the Bible many different ways. They won't come together when the basic rules for understanding written material are not being followed on the most important written material, the Bible. So what do people do? They decide the way to unity is by promoting fundamentals or essentials. Harmonize around a certain lower or even lowest common denominator, and call that Biblical unity. People who won't, they're divisive and heretics.
By the way, plain meaning of Scripture says premillennialism. Premillennialism is just another way of saying plain meaning of the text, or grammatical-historical interpretation. That's how you understand the Bible if you pick it up on the deserted island. It's not meant to be misunderstood. God wrote it. He said a child could understand it. Dispensationalism came along to defend premillennialism against amillennialism and covenant theology. Even when the words premillennialism and dispensationalism didn't exist, they already existed. They existed with those people who took the plain meaning of the text.
Covenant theology said it was fine to spiritualize. An axehead could be something else. A cloud could be something else. Almost anything could be something else that means something else, even a great range of different things. If that's how it goes with the truth, then why doesn't any opinion matter any less or more than any other? It doesn't!!!
Subjectivity works nicely with pragmatism. You want it to work, but Scripture gets in the way? In comes Gumby. You can craft a new position that will work for church growth or anything else that you need.
And, of course, who is the boss in subjectivity? You are. That's nice for you. You actually are not the boss, so that's a lie, but you can say that God is the boss, and still be the boss in reality. You do that by making Scripture mean what you want it to mean. And why not? That's what covenant theology did, which as all about defending amillennialism.
Postmodernism works really nicely with all this, don'tcha think?