This is not exactly my area, but I suspect it simply may not be anyone's area.
It is not clear from the research literature that speaking rhythmically does help get into a trance, mostly because it is not currently clear that "trance" is distinct from other forms of dissociation (though dissociation is often confusingly described as "trance-like" or variations thereof). The closest recent paper I could find (Becker-Blease, 2004), simply reports on subjectively reported associations between certain kinds of music and the experience of a "trance" state, but this does not answer the questions of why or whether speaking rhythmically induces dissociative states.
A non-paywalled review of dissociation and dissociative states in a clinical context can be found in a Review of Psychiatry chapter by Putnam, 1991. Putnam employs the following definition of dissociation:
Dissociation is a process that produces a discernible alteration in a person's thoughts, feelings or actions so that for a period of time certain information is not associated or integrated with other information as it normally or logically would be.
Unfortunately, while subsequent literature in the same line of research has tentatively described a difference between clinical and nonclinical dissociative experiences (Waller, Putnam and Carlson, 1996), this was only descriptive, and did not attempt to investigate ways of inducing dissociative states. The focus appears to have remained on clinical dissociation.
In conclusion, the literature and evidence currently does not seem to distinguish between the two possibilities that nonclinical dissociation either can or cannot be induced by rhythmic speech, and there does not seem to be any meaningful consensus or even particularly influential views on the cognitive processes underlying nonclinical dissociation. It simply does not seem to be an active area of psychological research.
Becker-Blease, K. A. (2004). Dissociative states through new age and electronic trance music. Journal of trauma & dissociation, 5(2), 89-100.
Putnam, F. W. (1991). Dissociative phenomena. Review of psychiatry, 10, 145-160.
Waller, N., Putnam, F. W., & Carlson, E. B. (1996). Types of dissociation and dissociative types: A taxometric analysis of dissociative experiences. Psychological Methods, 1(3), 300.