Strictly speaking, this is not a theory, but a hypothesis. In scientific terminology, a theory is a well-substantiated, unifying explanation for a set of verified, proven hypotheses. A hypothesis is a suggested explanation for an observable phenomenon, and this is what JEDP is. The Documentary Hypothesis, as originally proposed by Wellhausen, is no longer accepted by the majority of biblical scholars as definitive but, with various proposed modifications under consideration, it remains the best explanation we have for the development of the Pentateuch.
The only serious alternative to the JEDP hypothesis is the tradition that Moses was the author, or at least the main author, of the Pentateuch. For this to be a viable explanation, there ought to be evidence that Moses was a real, historical person and that he was writing from his own experience. This evidence that must be found outside the Pentateuch itself, and could be found by comparing the extensive Egyptian records that we have, against the Book of Exodus. However, Lester L. Grabbe says in Ancient Israel, page 85, there is nothing in Egyptian texts that could be related to the story in the Book of Exodus. Carol A. Redmount says, in 'Bitter lives', published in The Oxford History of the Biblical World, page 63, the biblical Exodus account was never intended to function or to be understood as history in the present-day sense of the word. Perhaps there is an underlying historical core in Exodus but we should expect that a participant in the Exodus would write an account that more closely reflects his experience.
Mark S. Smith says, in his preface to The Early History of God (page xxiii), the older source theory of the Pentateuch (the Documentary Hypothesis) had already come under serious fire when The Early History of God first appeared (First edition: 1990). He says the newer redactional model developed by E. Blume and extended by D. M. Carr on the biblical side, and studies of redaction in Gilgamesh by J. H. Tigay on the ancient Near Eastern side, have complicated source theory without abolishing it. While the death knell for source theory was sounded often over the course of the 1980s and 1990s, it has not been supplanted by a more persuasive model.
Joel S. Baden says, in 'The Re-Emergence of Source Criticism: The Neo-Documentary Hypothesis' that European scholarship abandoned the JEDP hypothesis as American scholars continued to support it. He says this situation is changing, as the Documentary Hypothesis is regaining its place as a viable, productive, and current approach to the Pentateuch. One of the main contributions of more recent source-critical work has been the identification and correction of the methodological problems that plagued earlier scholarship, contributing significantly if not primarily to the move away from the Documentary Hypothesis in Europe in recent generations.