An acyclic graph (or a tree structure) enables certain automatic layout algorithms. These algorithms are predictable by the user and are less distracting -- the key goal of any mindmap software is to not distract.
There's probably a semantic element of a hierarchy of ideas, too, but I am only equipped to comment on the math and not the psychology. :)
So if we were going to take the LaTeX approach, we basically write our mind maps as .g files and then lay them out using Graphviz's dotty? That could actually work (OmniGraffle, BTW, uses Graphviz I think to layout DAGs).
There's probably a semantic element of a hierarchy of ideas, too, but I am only equipped to comment on the math and not the psychology. :)